Translator Disclaimer
January 2015 Towards a criterion for slope stability of Fano manifolds along divisors
Kento Fujita
Osaka J. Math. 52(1): 71-93 (January 2015).

Abstract

We give a simple criterion for slope stability of Fano manifolds $X$ along divisors or smooth subvarieties. As an application, we show that $X$ is slope stable along an ample effective divisor $D\subset X$ unless $X$ is isomorphic to a projective space and $D$ is a hyperplane section. We also give counterexamples to Aubin's conjecture on the relation between the anticanonical volume and the existence of a Kähler--Einstein metric. Finally, we consider the case that $\dim X = 3$; we give a complete answer for slope (semi)stability along divisors of Fano threefolds.

Citation

Download Citation

Kento Fujita. "Towards a criterion for slope stability of Fano manifolds along divisors." Osaka J. Math. 52 (1) 71 - 93, January 2015.

Information

Published: January 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1327.14192
MathSciNet: MR3326603

Subjects:
Primary: 14J45
Secondary: 14L24, 32Q20

Rights: Copyright © 2015 Osaka University and Osaka City University, Departments of Mathematics

JOURNAL ARTICLE
23 PAGES


SHARE
Vol.52 • No. 1 • January 2015
Back to Top