Sasaki–Einstein metrics and K–stability

Collins, Tristan¹ ; Székelyhidi, Gábor²

¹ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States
² Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States

Geometry & topology, Tome 23 (2019) no. 3, pp. 1339-1413.

Résumé

We show that a polarized affine variety with an isolated singularity admits a Ricci flat Kähler cone metric if and only if it is K–stable. This generalizes the Chen–Donaldson–Sun solution of the Yau–Tian–Donaldson conjecture to Kähler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki–Einstein metrics.

Détail

DOI : 10.2140/gt.2019.23.1339

Classification : 32Q20, 53C25, 32Q26
Keywords: K–stability, Kähler–Einstein, Sasaki

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