## Osaka Journal of Mathematics

### Towards a criterion for slope stability of Fano manifolds along divisors

Kento Fujita

#### 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.

#### Article information

Source
Osaka J. Math., Volume 52, Number 1 (2015), 71-93.

Dates
First available in Project Euclid: 24 March 2015

https://projecteuclid.org/euclid.ojm/1427202873

Mathematical Reviews number (MathSciNet)
MR3326603

Zentralblatt MATH identifier
1327.14192

#### Citation

Fujita, Kento. Towards a criterion for slope stability of Fano manifolds along divisors. Osaka J. Math. 52 (2015), no. 1, 71--93. https://projecteuclid.org/euclid.ojm/1427202873

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