K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics
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Batyrev, V.V.: Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J. Algebr. Geom. 3, 493–535 (1994)
Berman, R.J.: Berndtsson, B.: Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties. Ann de la Fac des Sci de Toulouse. Série VI. Math. 4(4), (2013)
Berman, R.J., Boucksom, S., Guedj, V., Zeriahi, A.: A variational approach to complex Monge-Ampere equations. Publications Math. de l’IHÉS, 117(1), 179–245 (2013)
Berman, R.J., Eyssidieux, P., Boucksom, S., Guedj, V., Zeriahi, A.: Kähler-Einstein metrics and the Kähler-Ricci flow on log Fano varieties. arXiv:1111.7158
Berman, R.J., Hisamoto, T., Nyström, D.W.: Calabi type functionals, test configurations and geodesic rays (article in preparation)
Berman, R.J., Guenancia, H.: Kähler-Einstein metrics on stable varieties and log canonical pairs. Geom. Funct. Anal. 24(6), 1683–1730 (2014)
Berman, R.J., Witt Nystrom, D.: Complex optimal transport and the pluripotential theory of Kähler-Ricci solitons. arXiv:1401.8264
Berndtsson, B.: Curvature of vector bundles associated to holomorphic fibrations. Ann. Math. 169, 531–560 (2009)
Berndtsson, B.: Strict and nonstrict positivity of direct image bundles. Math. Zeitschrift 269(3–4), 1201–1218 (2011)
Berndtsson, B.: A Brunn-Minkowski type inequality for Fano manifolds and the Bando- Mabuchi uniqueness theorem. Inventiones Math. arXiv:1103.0923 (2014)
Berndtsson, B., Paun, M.: Bergman kernels and the pseudoeffectivity of relative canonical bundles. Duke Math. J. 145(2), 341–378 (2008)
Berndtsson, B., Paun, M.: A Bergman kernel proof of the Kawamata subadjunction theorem. arXiv:0804.3884
Campana, F., Guenancia, H., Păun, M.: Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields. Annales Scientifiques de l’École Normale Supérieure. série 4 46, fascicule 6 (2013)
Chen, X.: Space of Kähler metrics (IV): on the lower bound of the K-energy. arXiv:0809.4081v2
Chen, X., Tang, Y.: Test configuration and geodesic rays. Géométrie différentielle, physique mathématique, mathématiques et société. I. Astérisque 321, 139–167 (2008)
Chen, X., Donaldson, S., Sun, S.: Kähler-Einstein metrics on Fano manifolds, I: Approximation of metrics with cone singularities. J. Amer. Math. Soc. 28, 183–197 (2015)
Chen, X., Donaldson, S., Sun, S.: Kähler-Einstein metrics on Fano manifolds, II: Limits with cone angle less than $$2\pi $$ 2 π . J. Amer. Math. Soc. 28, 199–234 (2015)
Chen, X., Donaldson, S., Sun, S.: Kähler-Einstein metrics on Fano manifolds, III: Limits as cone angle approaches $$2\pi $$ 2 π and completion of the main proof. J. Amer. Math. Soc. 28, 235–278 (2015)
Csiszár, I., Körner, J.: Information Theory: Coding Theorems for Discrete Memoryless Systems. Cambridge University Press, Cambridge (2011)
Darvas, T., He, W.: Geodesic Rays and Kähler-Ricci Trajectories on Fano Manifolds. arXiv:1411.0774
Demailly, J.-P., Kollar, J.: Semi-continuity of complex singularity exponents and Kähler- Einstein metrics on Fano orbifolds. Ann. Sci. École Norm. Sup. 34(4), 525–556 (2001)
Ding, W.Y.: Remarks on the existence problem of positive Kähler-Einstein metrics. Math. Ann 282, 463–471 (1988)
Ding, W.Y., Tian, G.: Kähler-Einstein metrics and the generalized Futaki invariant. Invent. Math. 110(2), 315–335 (1992)
Donaldson, S.K.: Symmetric spaces, Kähler geometry and Hamiltonian dynamics. In: Northern California Symplectic Geometry Seminar, vol. 196 of Amer. Math. Soc. Transl. Ser. 2, pp. 13–33. Amer. Math. Soc., Providence, RI (1999)
Donaldson, S.K.: Scalar curvature and stability of toric varities. J. Differ. Geom. 62, 289–349 (2002)
Donaldson, S.K.: Some numerical results in complex differential geometry. Pure Appl. Math. Q. 5(2), 571–618 (2009). (Special Issue: In honor of Friedrich Hirzebruch)
Donaldson, S.K.: Kahler metrics with cone singularities along a divisor. Essays in mathematics and its applications, pp. 49–79. Springer, Heidelberg (2012)
Donaldson, S.K., Sun, S.: Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry. Acta Math. 213, 63–106
Eyssidieux, P., Guedj, V., Zeriahi, A.: Singular Kähler-Einstein metrics. J. Am. Math. Soc. 22, 607–639 (2009)
Greuel, G.M., Lossen, C., Shustin, E.: Introduction to Singularities and Deformations. Springer, New York (2007)
Guedj, V., Zeriahi, A.: Intrinsic capacities on compact Kähler manifolds. J. Geom. Anal. 15(4), 607–639 (2005)
Guenancia, H., Păun, M.: Conic singularities metrics with prescribed Ricci curvature: the case of general cone angles along normal crossing divisors. arXiv:1307.6375
He, W.: $${\cal F}$$ F -functional and geodesic stability. arXiv:1208.1020
Jeffres, T.D., Mazzeo, R., Rubinstein, Y.A.: Kähler-Einstein metrics with edge singularities. arXiv:1105.5216 (2011)
Hartshorne, R.: Algebraic Geometry. Graduate Texts in Math, vol. 52. Springer-Verlag, Berlin (2006)
Hisamoto, T.: On the limit of spectral measures associated to a test configuration. Preprint
Kawamata, Y.: Characterization of abelian varieties. Compositio Math. 43(2), 253–276 (1981)
Kollar, J.: Singularities of pairs. Algebraic Geom—Santa Cruz. In: Proceedings of Symposia Pure Mathematics 62, Part 1, pp. 221–287. Amer. Math. Soc., Providence, RI (1995)
Kreuzer, M., Skarke, H.: PALP: a package for analyzing lattice polytopes with applications to toric geometry. Comput. Phys. Commun. 157, 87–106 (2004)
Li, C.: Remarks on logarithmic K-stability. arXiv:math/1104042
Li, C., Xu, C.: Special test configurations and K-stability of Fano varieties. Ann. Math. 180, 197–232 (2014). arXiv:1111.5398
Mabuchi, T.: An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, I. Invent. Math. 159(2), 225–243 (2005). (MR 2116275)
Mabuchi, T.: K-stability of constant scalar curvature polarization. arXiv:0812.4093
Mabuchi, T.: A stronger concept of K-stability. arXiv:0910.4617
Moriwaki, A.: The continuity of Deligne’s pairing. Internat. Math. Res. Notices 19, 1057–1066 (1999)
Morrison, I.: GIT Constructions of Moduli Spaces of Stable Curves and Maps. Riemann Surfaces and Their Moduli Spaces, Surv. Differ. Geom., vol. 14, pp. 315–369. Int. Press, Somerville (2009)
Kempf, G., Ness, L.: The Length of Vectors in Representation Spaces. Lecture Notes in Math., vol. 732, pp. 233–244. Springer, New York (1978)
Nyström, D.W.: Test configurations and Okounkov bodies. Compos. Math. arXiv:1001.3286 (2010)
Odaka, Y.: A generalization of the Ross-Thomas slope theory. Osaka J. Math. 50(1), 171–185 (2013)
Odaka, Y., Sun, S.: Testing log K-stability by blowing up formalism. arXiv:1112.1353
Odaka, Y., Spotti, S., Sun, S.: Compact moduli spaces of del pezzo surfaces and Kähler-Einstein metrics. arXiv:1210.0858
Odaka, Y.: On the moduli of Kahler-Einstein Fano manifolds. Proceeding of Kinosaki algebraic geometry symposium. arXiv:1211.4833 (2013)
Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. arXiv:math/0211159
Paul, S., Tian, G.: CM stability and the generalized Futaki invariant I. arXiv:math/0605278 . CM stability and the generalized Futaki invariant II. Astérisque No. 328 (2009)
Paul, S.T.: Hyperdiscriminant polytopes, Chow polytopes, and Mabuchi energy asymptotics. Ann. Math. 175(1), 255–296 (2012)
Păun, M.: Takayama, S: Positivity of twisted relative pluricanonical bundles and their direct images. arXiv:1409.5504
Phong, D.H., Ross, J., Sturm, J.: Deligne pairings and the Knudsen-Mumford expansion. J. Differ. Geom. 78(3), 475–496 (2008)
Phong, D.H., Sturm, J.: Test configurations for K-stability and geodesic rays. J. Symp. Geom. 5, 221–247 (2007)
Phong, D.H., Song, J., Sturm, J., Weinkove, B.: The Moser-Trudinger inequality on Kähler- Einstein manifolds. Am. J. Math. 130(4), 1067–1085 (2008)
Phong, D.H., Sturm, J.: Regularity of geodesic rays and Monge-Ampère equations. Proc. Am. Math. Soc. 138(10), 3637–3650 (2010)
Phong, D.H., Sturm, J.: Lectures on stability and constant scalar curvature. Handbook of geometric analysis, No. 3, Adv. Lect. Math. (ALM), vol. 14, pp. 357–436. Int. Press, Somerville (2010)
Ross, J., Thomas, R.: A study of the Hilbert-Mumford criterion for the stability of projective varieties. J. Algebraic Geom. 16, 201–255 (2007)
Székelyhidi, G.: The partial $$C^{0}$$ C 0 -estimate along the continuity method. arXiv:1310.8471 (2013)
Stoppa, J.: K-stability of constant scalar curvature Kähler manifolds. Adv. Math. 221(4), 1397–1408 (2009)
Stoppa, J.: A note on the definition of K-stability. arXiv:1111.5826
Stoppa, J., Székelyhidi, G.: Relative K-stability of extremal metrics. J. Eur. Math. Soc. (JEMS) 13(4), 899–909 (2011)
Tian, G.: On Calabi’s conjecture for complex surfaces with positive first Chern class. Invent. Math. 101(1), 101–172 (1990)
Tian, G.: Existence of Einstein metrics on Fano manifolds. In: Metric and Differential Geometry Progress in Mathematics, vol. 297, Part 1, pp. 119–159 (2012)
Tian, G., Zhu, X.: Convergence of Kähler-Ricci flow on Fano manifolds, II. arXiv:1102.4798
Tian, G., Zhang, S.: Zhang, Z: Zhu, X: Supremum of Perelman’s entropy and Kähler-Ricci flow on a Fano manifold. arXiv:1107.4018
Tosatti, V.: Families of Calabi-Yau manifolds and canonical singularities. arXiv:1311.4845 (2013)
Zhang, S.: Heights and reductions of semi-stable varieties. Compositio Math. 104(1), 77–105 (1996)