biblio.tex

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@Book{mumford1994,
  title     = {Geometric invariant theory},
  publisher = {Springer Science \& Business Media},
  year      = {1994},
  author    = {Mumford, David and Fogarty, John and Kirwan, Frances},
  volume    = {34},
}

@article{fujita2018k,
  title={On the K-stability of Fano varieties and anticanonical divisors},
  author={Fujita, Kento and Odaka, Yuji and others},
  journal={Tohoku Mathematical Journal},
  volume={70},
  number={4},
  pages={511--521},
  year={2018},
  publisher={Tohoku University}
}


@Book{hartshorne2013,
  title     = {Algebraic geometry},
  publisher = {Springer Science \& Business Media},
  year      = {2013},
  author    = {Hartshorne, Robin},
  volume    = {52},
}

@article{petersen2011torus,
  title={Torus invariant divisors},
  author={Petersen, Lars and S{\"u}{\ss}, Hendrik},
  journal={Israel Journal of Mathematics},
  volume={182},
  number={1},
  pages={481--504},
  year={2011},
  publisher={Springer}
}

@article{li2009greatest,
  title={Greatest lower bounds on Ricci curvature for toric Fano manifolds},
  author={Li, Chi},
  journal={arXiv preprint arXiv:0909.3443},
  year={2009}
}


@article{tian1992stability,
  title={On stability of the tangent bundles of {F}ano varieties},
  author={Tian, Gang},
  journal={Internat. J. Math},
  volume={3},
  number={3},
  pages={401--413},
  year={1992}
}

@article{donaldson2008kahler,
  title={Kahler geometry on toric manifolds, and some other manifolds with large symmetry},
  author={Donaldson, Simon K},
  journal={arXiv preprint arXiv:0803.0985},
  year={2008}
}


@Article{baker2012,
  author  = {B{\"a}ker, Hendrik and Hausen, J{\"u}rgen and Keicher, Simon},
  title   = {On {C}how quotients of torus actions},
  journal = {Michigan Math. J.},
  year    = {2015},
  volume  = {64},
  number  = {3},
  pages   = {451--473},
}

@Article{kapranov1993,
  author  = {Kapranov, Mikhail M},
  title   = {Chow quotients of {G}rassmannians. {I}},
  journal = {Adv. Soviet Math},
  year    = {1993},
  volume  = {16},
  number  = {2},
  pages   = {29--110},
}

@article{Aubin1976,
  title={Equations du type Monge-Ampere sur la varietes kahleriennes compactes},
  author={Aubin, Thierry},
  journal={CR Acad. Sci. Paris},
  volume={283},
  pages={119--121},
  year={1976}
}

@article{Yau1977,
  title={Calabi's conjecture and some new results in algebraic geometry},
  author={Yau, Shing-Tung},
  journal={Proceedings of the National Academy of Sciences},
  volume={74},
  number={5},
  pages={1798--1799},
  year={1977},
  publisher={National Acad Sciences}
}

@article{yau1975,
  title={Harmonic functions on complete Riemannian manifolds},
  author={Yau, Shing-Tung},
  journal={Communications on Pure and Applied Mathematics},
  volume={28},
  number={2},
  pages={201--228},
  year={1975},
  publisher={Wiley Online Library}
}


@article{CDS12,
  title={K{\"a}hler-{E}instein metrics and stability},
  author={Chen, Xiu-Xiong and Donaldson, Simon and Sun, Song},
  journal={Int. Math.Res. Not. IMRN},
  number={8},
  pages={2119-2125},
  year={2014}
}

@article{CDS13,
  title={K{\"a}hler-{E}instein metrics on {F}ano manifolds. {I}{I}{I}: {L}imits as cone angle approaches $2 \pi$ and completion of the main proof},
  author={Chen, Xiuxiong and Donaldson, Simon and Sun, Song},
  journal={Journal of the American Mathematical Society},
  volume={28},
  number={1},
  pages={235--278},
  year={2015}
}

@article{Tian87,
  title={On {K}{\"a}hler-{E}instein metrics on certain {K}{\"a}hler manifolds with $c_1 (M)> 0$},
  author={Tian, Gang},
  journal={Inventiones mathematicae},
  volume={89},
  number={2},
  pages={225-246},
  year={1987},
  publisher={Springer}
}

@article{Su13,
title = {{K}{\"a}hler-{E}instein metrics on symmetric {Fano} {$T$-varieties} },
journal = {Advances in Mathematics},
volume = {246},
pages = {100 - 113},
year = {2013},
author = {Hendrik S{\"u}{\ss}}
}

@article{batyrev99,
  title={Einstein-{K}{\"a}hler metrics on symmetric toric {F}ano manifolds},
  author={Batyrev, Victor V and Selivanova, Elena N},
  journal={{J}. {R}eine {A}ngew. {M}ath.},
  year={1999},
  number={512},
  pages={225 - 236}
}

@article{cheltsov08,
  title={Log canonical thresholds of smooth {F}ano threefolds},
  author={Cheltsov, Ivan A and Shramov, Konstantin A},
  journal={Russian Mathematical Surveys},
  volume={63},
  number={5},
  pages={859},
  year={2008},
  publisher={IOP Publishing}
}

@inproceedings{demailly2001,
  title={Semi-continuity of complex singularity exponents and {K}{\"a}hler-{E}instein metrics on {F}ano orbifolds},
  author={Demailly, Jean-Pierre and Koll{\'a}r, J{\'a}nos},
  booktitle={Annales scientifiques de l'Ecole normale sup{\'e}rieure},
  volume={34},
  number={4},
  pages={525--556},
  year={2001}
}



@unpublished{suess18-2,
   author = {S{\"u}{\ss}, Hendrik},
   url={http://arxiv.org/abs/1810.00981},
   title="{Orbit spaces of maximal torus actions on oriented {G}rassmannians of planes}",
   journal={arXiv preprint arXiv:1810.00981},
   year={2018}
}

@article{wang2004,
  title={{K}{\"a}hler--{R}icci solitons on toric manifolds with positive first {C}hern class},
  author={Wang, Xu-Jia and Zhu, Xiaohua},
  journal={Advances in Mathematics},
  volume={188},
  number={1},
  pages={87--103},
  year={2004},
  publisher={Elsevier}
}

@article{ilten2015,
  title={K-stability for {F}ano manifolds with torus action of complexity 1},
  author={Ilten, Nathan and S{\"u}{\ss}, Hendrik},
  journal={Duke Math. J.},
  volume={166},
  number={1},
  pages={177-204},
  year={2017}
}

@incollection{kempf1979,
  title={The length of vectors in representation spaces},
  author={Kempf, George and Ness, Linda},
  booktitle={Algebraic geometry},
  pages={233--243},
  year={1979},
  publisher={Springer}
}

@article{kirwan,
  title={Partial desingularisations of quotients of nonsingular varieties and their {B}etti numbers},
  author={Kirwan, Frances Clare},
  journal={Annals of mathematics},
  volume={122},
  number={1},
  pages={41--85},
  year={1985},
  publisher={JSTOR}
}

@article{li06,
  title={Wonderful compactification of an arrangement of subvarieties},
  author={Li, Li},
  journal={Michigan Math. J. },
  volume={58},
  number={2},
  pages={535-563},
  year={2009}
}

@article{del2016,
  title={K-Stability of {F}ano spherical varieties},
  author={Delcroix, Thibaut},
  journal={arXiv preprint arXiv:1608.01852},
  year={2016}
}

@article{guillemin1982convexity,
  title={Convexity properties of the moment mapping},
  author={Guillemin, Victor and Sternberg, Shlomo},
  journal={Inventiones mathematicae},
  volume={67},
  number={3},
  pages={491--513},
  year={1982},
  publisher={Springer}
}

@article{atiyah1982convexity,
  title={Convexity and commuting {H}amiltonians},
  author={Atiyah, Michael Francis},
  journal={Bulletin of the London Mathematical Society},
  volume={14},
  number={1},
  pages={1--15},
  year={1982},
  publisher={Wiley Online Library}
}

@article{hausen2018torus,
  title={On torus actions of higher complexity},
  author={Hausen, Juergen and Hische, Christoff and Wrobel, Milena},
  journal={arXiv preprint arXiv:1802.00417},
  year={2018}
}

@article{Calabi82,
	title={Extremal {K}{\"a}hler metrics},
	author={Calabi, Eugenio},
	journal={Seminar on Differential Geometry (S. T. Yau, ed.), },
	publisher={Princeton},
	year={1982}
}

@book{szebook,
  title={An introduction to extremal {K}{\"a}hler metrics},
  author={Sz{\'e}kelyhidi, G{\'a}bor},
  volume={152},
  year={2014},
  publisher={American Mathematical Soc.}
}

@article{Matsushima,
title={Remarks on {K}{\"a}hler-{E}instein manifolds},
author={{M}atsushima, {Y}ozo},
journal={Nagoya {M}ath. {J}.},
volume={46},
year={1972},
pages={161-173}
}

@article{matsushima1957structure,
  title={Sur la Structure du Groupe d’Hom{\'e}omorphismes Analytiques d’une Certaine Vari{\'e}t{\'e} Kaehl{\'e}rinne},
  author={Matsushima, Yoz{\^o}},
  journal={Kähler-Einstein metrics on symmetric general arrangement varietiesNagoya Mathematical Journal},
  volume={11},
  pages={145--150},
  year={1957},
  publisher={Cambridge University Press}
}

@article{nadel1990multiplier,
  title={Multiplier ideal sheaves and Kahler-Einstein metrics of positive scalar curvature},
  author={Nadel, Alan Michael},
  journal={Annals of Mathematics},
  pages={549--596},
  year={1990},
  publisher={JSTOR}
}

@inproceedings{demaily2001semi,
  title={Semi-continuity of complex singularity exponents and K{\"a}hler-Einstein metrics on Fano orbifolds},
  author={Demailly, Jean-Pierre and Koll{\'a}r, J{\'a}nos},
  booktitle={Annales scientifiques de l'Ecole normale sup{\'e}rieure},
  volume={34},
  number={4},
  pages={525--556},
  year={2001}
}

@article{rubinstein2009,
  title={On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow},
  author={Rubinstein, Yanir},
  journal={Transactions of the American Mathematical Society},
  volume={361},
  number={11},
  pages={5839--5850},
  year={2009}
}

@article{rubinstein2008,
  title={Some discretizations of geometric evolution equations and the Ricci iteration on the space of K{\"a}hler metrics},
  author={Rubinstein, Yanir A},
  journal={Advances in Mathematics},
  volume={218},
  number={5},
  pages={1526--1565},
  year={2008},
  publisher={Elsevier}
}


@article{szekelyhidi2011,
  title={Greatest lower bounds on the Ricci curvature of Fano manifolds},
  author={Sz{\'e}kelyhidi, G{\'a}bor},
  journal={Compositio Mathematica},
  volume={147},
  number={1},
  pages={319--331},
  year={2011},
  publisher={London Mathematical Society}
}

@article{li2017,
  title={K-semistability is equivariant volume minimization},
  author={Li, Chi and others},
  journal={Duke Mathematical Journal},
  volume={166},
  number={16},
  pages={3147--3218},
  year={2017},
  publisher={Duke University Press}
}


@article{li2011,
  title={Greatest lower bounds on Ricci curvature for toric Fano manifolds},
  author={Li, Chi},
  journal={Advances in Mathematics},
  volume={226},
  number={6},
  pages={4921-4932},
  year={2011}
}

@article{cheltsov2019basis,
  title={Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces},
  author={Cheltsov, Ivan A and Rubinstein, Yanir A and Zhang, Kewei},
  journal={Selecta Mathematica},
  volume={25},
  number={2},
  pages={34},
  year={2019},
  publisher={Springer}
}

@article{yau1978ricci,
  title={On the ricci curvature of a compact k{\"a}hler manifold and the complex monge-amp{\'e}re equation, I},
  author={Yau, Shing-Tung},
  journal={Communications on pure and applied mathematics},
  volume={31},
  number={3},
  pages={339--411},
  year={1978},
  publisher={Wiley Online Library}
}

@article{chen2015kahler1,
  title={K{\"a}hler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities},
  author={Chen, Xiuxiong and Donaldson, Simon and Sun, Song},
  journal={Journal of the American Mathematical Society},
  volume={28},
  number={1},
  pages={183--197},
  year={2015}
}

@article{chen2015kahler2,
  title={K{\"a}hler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2𝜋},
  author={Chen, Xiuxiong and Donaldson, Simon and Sun, Song},
  journal={Journal of the American Mathematical Society},
  volume={28},
  number={1},
  pages={199--234},
  year={2015}
}

@article{chen2015kahler3,
  title={K{\"a}hler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2𝜋 and completion of the main proof},
  author={Chen, Xiuxiong and Donaldson, Simon and Sun, Song},
  journal={Journal of the American Mathematical Society},
  volume={28},
  number={1},
  pages={235--278},
  year={2015}
}

@article{berman2014complex,
  title={Complex optimal transport and the pluripotential theory of K$\backslash$" ahler-Ricci solitons},
  author={Berman, Robert J and Nystrom, David Witt},
  journal={arXiv preprint arXiv:1401.8264},
  year={2014}
}


@article{berman2016k,
  title={K-polystability of Q-Fano varieties admitting K{\"a}hler-Einstein metrics},
  author={Berman, Robert J},
  journal={Inventiones mathematicae},
  volume={203},
  number={3},
  pages={973--1025},
  year={2016},
  publisher={Springer}
}

@article{stoppa2008k,
  title={K-stability of constant scalar curvature K$\backslash$" ahler manifolds},
  author={Stoppa, Jacopo},
  journal={arXiv preprint arXiv:0803.4095},
  year={2008}
}

@article{tian1997kahler,
  title={K{\"a}hler-Einstein metrics with positive scalar curvature},
  author={Tian, Gang},
  journal={Inventiones Mathematicae},
  volume={130},
  number={1},
  pages={1--37},
  year={1997},
  publisher={Springer}
}

@article{poincare1908uniformisation,
  title={Sur l'uniformisation des fonctions analytiques},
  author={Poincar{\'e}, Henri},
  journal={Acta mathematica},
  volume={31},
  number={1},
  pages={1--63},
  year={1908},
  publisher={Springer}
}

@article{koebe1909uniformisierung,
  title={{\"U}ber die Uniformisierung der algebraischen Kurven. I},
  author={Koebe, Paul},
  journal={Mathematische Annalen},
  volume={67},
  number={2},
  pages={145--224},
  year={1909},
  publisher={Springer}
}

@article{altmann2006polyhedral,
  title={Polyhedral divisors and algebraic torus actions},
  author={Altmann, Klaus and Hausen, J{\"u}rgen},
  journal={Mathematische Annalen},
  volume={334},
  number={3},
  pages={557--607},
  year={2006},
  publisher={Springer}
}


@article{koebe1910uniformisierung,
  title={{\"U}ber die Uniformisierung der algebraischen Kurven. II},
  author={Koebe, Paul},
  journal={Mathematische Annalen},
  volume={69},
  number={1},
  pages={1--81},
  year={1910},
  publisher={Springer}
}

@article{cable2018classification,
  title={On the classification of K{\"a}hler--Ricci solitons on Gorenstein del Pezzo surfaces},
  author={Cable, Jacob and S{\"u}{\ss}, Hendrik},
  journal={European Journal of Mathematics},
  volume={4},
  number={1},
  pages={137--161},
  year={2018},
  publisher={Springer}
}

@article{cable2019greatest,
  title={Greatest lower bounds on Ricci curvature for Fano {T}-manifolds of complexity one},
  author={Cable, Jacob},
  journal={Bulletin of the London Mathematical Society},
  volume={51},
  number={1},
  pages={34--42},
  year={2019},
  publisher={Wiley Online Library}
}

@unpublished{cable2019general,
   author = {Cable, Jacob},
   url={http://arxiv.org/abs/arXiv:1906.10080},
   title="{K{\"a}hler-{E}instein metrics on symmetric general arrangement varieties}",
   journal={arXiv preprint arXiv:1906.10080},
   year={2019}
}

@article{mori1981classification,
  title={Classification of Fano 3-folds with B 2≥ 2},
  author={Mori, Shigefumi and Mukai, Shigeru},
  journal={manuscripta mathematica},
  volume={36},
  number={2},
  pages={147--162},
  year={1981},
  publisher={Springer}
}

@article{suss2013fano,
  title={Fano threefolds with 2-torus action-a picture book},
  author={S{\"u}{\ss}, Hendrik},
  journal={arXiv preprint arXiv:1308.2379},
  year={2013}
}

@article{yao2017,
  title={Greatest lower bounds on Ricci curvature of homogeneous toric bundles},
  author={Yao, Yi},
  journal={International Journal of Mathematics},
  volume={28},
  number={04},
  pages={1750024},
  year={2017},
  publisher={World Scientific}
}

@incollection{da2006symplectic,
  title={Symplectic geometry},
  author={da Silva, Ana Cannas},
  booktitle={Handbook of differential geometry},
  volume={2},
  pages={79--188},
  year={2006},
  publisher={Elsevier}
}


@article{delcroix2017,
  title={K{\"a}hler--Einstein metrics on group compactifications},
  author={Delcroix, Thibaut},
  journal={Geometric and Functional Analysis},
  volume={27},
  number={1},
  pages={78--129},
  year={2017},
  publisher={Springer}
}


@article{datar2016kahler,
  title={K{\"a}hler--Einstein metrics along the smooth continuity method},
  author={Datar, Ved and Sz{\'e}kelyhidi, G{\'a}bor},
  journal={Geometric and Functional Analysis},
  volume={26},
  number={4},
  pages={975--1010},
  year={2016},
  publisher={Springer}
}


@article{calabi54,
  title={The space of {K}{\"a}hler metrics},
  author={Calabi, Eugenio},
  journal={Proceedings of the International Congress of Mathematicians},
  volume={2},
  pages={206--207},
  year={1956}
}

@article{calabi57,
  title={On {K}{\"a}hler manifolds with vanishing canonical class},
  author={Calabi, Eugenio},
  journal={Princeton Mathematical Series},
  number={12},
  pages={78--89},
  year={1957}
}


@article{tian1987kahler,
  title={On K{\"a}hler-Einstein metrics on certain K{\"a}hler manifolds withc 1 (M)> 0},
  author={Tian, Gang},
  journal={Inventiones mathematicae},
  volume={89},
  number={2},
  pages={225--246},
  year={1987},
  publisher={Springer-Verlag}
}

@article{futaki1983obstruction,
  title={An obstruction to the existence of Einstein K{\"a}hler metrics},
  author={Futaki, Akito},
  journal={Inventiones mathematicae},
  volume={73},
  number={3},
  pages={437--443},
  year={1983},
  publisher={Springer}
}

@article{suss2013kahler,
  title={K{\"a}hler--Einstein metrics on symmetric Fano T-varieties},
  author={S{\"u}{\ss}, Hendrik},
  journal={Advances in Mathematics},
  volume={246},
  pages={100--113},
  year={2013},
  publisher={Elsevier}
}

@Comment{jabref-meta: databaseType:bibtex;}