Existence of Kähler-Ricci solitons on smoothable Q-Fano varieties

Advances in Mathematics - Tập 391 - Trang 107975 - 2021
Yan Li1
1Institute of Mathematics, Hunan University, Changsha, China

Tài liệu tham khảo

Bedford, 1982, A new capacity for plurisubharmonic functions, Acta Math., 149, 1, 10.1007/BF02392348 Berman, 2016, K-polystable of Q-Fano varieties admitting Kähler-Einstein metrics, Invent. Math., 203, 973, 10.1007/s00222-015-0607-7 Berman Berman Berman, 2012, A variational approach to complex Monge-Ampère equations, Publ. Math. IHÉS, 179 Berman, 2019, Kähler-Einstein metrics and Kähler-Ricci flow on log Fano varieties, J. Reine Angew. Math., 10.1515/crelle-2016-0033 Berndtsson, 2011, Strict and non strict positivity of direct image bundles, Math. Z., 269, 1201, 10.1007/s00209-010-0783-5 Berndtsson, 2015, A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry, 200, 149 Blocki, 2007, On regularization of plurisubharmonic functions on manifolds, Proc. Am. Math. Soc., 135, 2089, 10.1090/S0002-9939-07-08858-2 Boucksom, 2010, Monge-Ampère equations in big cohomology classes, Acta Math., 205, 199, 10.1007/s11511-010-0054-7 Chen, 2015, Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities, J. Am. Math. Soc., 28, 183, 10.1090/S0894-0347-2014-00799-2 Chen, 2015, Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2π, J. Am. Math. Soc., 28, 199, 10.1090/S0894-0347-2014-00800-6 Chen, 2015, Kähler-Einstein metrics on Fano manifolds, III: Limits as cone angle approaches 2π and completion of the main proof, J. Am. Math. Soc., 28, 235, 10.1090/S0894-0347-2014-00801-8 Darvas Datar, 2016, Kähler-Einstein metric along the smooth continuity method, Geom. Funct. Anal., 26, 975, 10.1007/s00039-016-0377-4 Donaldson, 2014, Gromov-Hausdorff limits of Kähler manifolds and algebraic geometry, Acta Math., 213, 63, 10.1007/s11511-014-0116-3 Evans, 1982, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Commun. Pure Appl. Math., 35, 333, 10.1002/cpa.3160350303 Eyssidieux, 2009, Singular Kähler-Einstein metrics, J. Am. Math. Soc., 22, 607, 10.1090/S0894-0347-09-00629-8 Griffiths, 1978 Guedj, 2017 Kollár, 1998, Birational Geometry of Algebraic Varieties, vol. 134 Krylov, 1982, Boundedly inhomogeneous elliptic and parabolic equations, Izv. Akad. Nauk SSSR, Ser. Mat., 46, 487 La Nave, 2017, Bounding diameter of singular Kähler metric, Am. J. Math., 169, 1693, 10.1353/ajm.2017.0042 Li, 2015, Yau-Tian-Donaldson correspondence for K-semistable Fano manifolds, J. Reine Angew. Math. Li Li Li, 2014, Conical K ähler-Einstein metrics revisited, Commun. Math. Phys., 331, 927, 10.1007/s00220-014-2123-9 Li Li, 2019, On the proper moduli spaces of smoothable Kähler-Einstein Fano manifolds, Duke Math. J., 168, 1387, 10.1215/00127094-2018-0069 Li, 2020, The continuity equation with cusp singularities, Math. Ann., 376, 729, 10.1007/s00208-018-1752-2 Mabuchi, 2002, Heat kernel estimates and the Green functions on multiplier Hermitian manifolds, Tohoku Math. J., 54, 259, 10.2748/tmj/1113247566 Mabuchi, 2003, Multiplier Hermitian structures on Kähler manifolds, Nagoya Math. J., 170, 73, 10.1017/S0027763000008540 Odaka, 2015, Compact moduli spaces of Kähler-Einstein Fano varieties, Publ. Res. Inst. Math. Sci., 51, 549, 10.4171/PRIMS/164 Odaka, 2016, Compact moduli spaces of Del Pezzo surfaces and Kähler-Einstein metrics, J. Differ. Geom., 102, 127, 10.4310/jdg/1452002879 Phong, 2010, The Dirichlet problem for degenerate complex Monge-Ampère equations, Commun. Anal. Geom., 18, 145, 10.4310/CAG.2010.v18.n1.a6 Phong, 2015, Degeneration of Kähler-Ricci solitons on Fano manifolds, Univ. Iagel. Acta Math., 52, 29 Rong, 2011, Continuity of extremal transitions and flops for Calabi-Yau manifolds, J. Differ. Geom., 82, 233 Rubinstein, 2008, Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kähler metrics, Adv. Math., 218, 1526, 10.1016/j.aim.2008.03.017 Song Song Spotti, 2014, Deformations of nodal Kähler-Einstein del Pezzo surfaces with discrete automorphism groups, J. Lond. Math. Soc. (2), 89, 539, 10.1112/jlms/jdt076 Spotti Spotti, 2016, Existence and deformations of Kähler-Einstein metrics on smoothable Q-Fano varieties, Duke Math. J., 165, 3043, 10.1215/00127094-3645330 Székelyhidi, 2016, The partial C0-estimate along the continuity method, J. Am. Math. Soc., 29, 537, 10.1090/jams/833 Tian, 1987, Kähler-Einstein metrics on certain Kähler manifolds with C1(M)>0, Invent. Math., 89, 225, 10.1007/BF01389077 Tian, 1997, Kähler-Einstein metrics with positive scalar curvature, Invent. Math., 130, 1, 10.1007/s002220050176 Tian, 2015, K-stability and Kähler-Einstein metrics, Commun. Pure Appl. Math., 68, 1085, 10.1002/cpa.21578 Tian, 2012, Degeneration of Kähler-Ricci solitons, Int. Math. Res. Not., 5, 957, 10.1093/imrn/rnr036 Tian, 2016, Convergence of Kähler-Ricci flow on lower dimension algebraic manifold of general type, Int. Math. Res. Not., 21, 6493, 10.1093/imrn/rnv357 Tian, 2000, Uniqueness of Kähler-Ricci solitons, Acta Math., 184, 271, 10.1007/BF02392630 Wang, 2013, On the structure of spaces with Bakry-Émery Ricci curvature bounded below, J. Reine Angew. Math. Wei, 2009, Comparison geometry for the Bakry-Émery Ricci tensor, J. Differ. Geom., 83, 377, 10.4310/jdg/1261495336 Zhu, 2000, Kähler-Ricci soliton-typed equations on compact complex manifold with C1(M)>0, J. Geom. Anal., 10, 759, 10.1007/BF02921996