Alpha Invariants and K-Stability for General Polarizations of Fano Varieties
Accepted version
Peer-reviewed
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Repository DOI
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Authors
Dervan, Ruadhaí
Abstract
We provide a sufficient condition for polarisations 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 polarisation. This generalises a result of Odaka-Sano in the anti-canonically polarised case, which is the algebraic counterpart of Tian’s analytic criterion implying the existence of a K¨ahler-Einstein metric. As an application, we give new K-stable polarisations of a general degree one del Pezzo surface. We also prove a corresponding result for log K-stability.
Description
Keywords
4901 Applied Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
International Mathematics Research Notices
Conference Name
Journal ISSN
1073-7928
1687-0247
1687-0247
Volume Title
2015
Publisher
Oxford University Press (OUP)
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/J002062/1)
Supported by a studentship associated to an EPSRC Career Acceleration Fellowship (EP/J002062/1)