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)

[img] Text
306511.pdf - Accepted Version



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
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 (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

University Staff: Request a correction | Enlighten Editors: Update this record