Alpha invariants and K-Stability for general polarizations of Fano varieties

Dervan, R. (2014) Alpha invariants and K-Stability for general polarizations of Fano varieties. International Mathematics Research Notices, 2015(16), pp. 7162-7189. (doi: 10.1093/imrn/rnu160)

Abstract

We provide a sufficient condition for polarizations of Fano varieties to be K-stable in terms of Tian's alpha invariant, which uses the log canonical threshold to measure singularities of divisors in the linear system associated to the polarization. This generalizes a result of Odaka–Sano in the anti-canonically polarized case, which is the algebraic counterpart of Tian's analytic criterion implying the existence of a Kähler–Einstein metric. As an application, we give new K-stable polarizations of a general degree 1 del Pezzo surface. We also prove a corresponding result for log K-stability.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Dervan, Dr Ruadhaí
• Authors: Dervan, R.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Copyright Holders: Copyright © The Author(s) 2014
• First Published: First published in International Mathematics Research Notices 2015(16):7162–7189
• Publisher Policy: Reproduced in accordance with the publisher copyright policy