Kähler–Ricci flow, Kähler–Einstein metric, and K–stability

Chen, Xiuxiong¹ ; Sun, Song² ; Wang, Bing³

¹ School of Mathematics, University of Science and Technology of China, Hefei, Anhui, China, Department of Mathematics, Stony Brook University, Stony Brook, NY, United States
² Department of Mathematics, University of California, Berkeley, Berkeley, CA, United States, Department of Mathematics, Stony Brook University, Stony Brook, NY, United States
³ School of Mathematics, University of Science and Technology of China, Hefei, Anhui, China, Department of Mathematics, University of Wisconsin-Madison, Madison, WI, United States

Geometry & topology, Tome 22 (2018) no. 6, pp. 3145-3173.

Résumé

We prove the existence of a Kähler–Einstein metric on a K–stable Fano manifold using the recent compactness result on Kähler–Ricci flows. The key ingredient is an algebrogeometric description of the asymptotic behavior of Kähler–Ricci flow on Fano manifolds. This is in turn based on a general finite-dimensional discussion, which is interesting on its own and could potentially apply to other problems. As one application, we relate the asymptotics of the Calabi flow on a polarized Kähler manifold to K–stability, assuming bounds on geometry.

Détail

DOI : 10.2140/gt.2018.22.3145

Classification : 53C25, 53C44, 14J45
Keywords: Kähler Ricci flow, convergence, uniqueness, Fano manifold, K–stability

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