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Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
- K. Fujita
- Mathematics
- 19 August 2015
abstract:We show that any $n$-dimensional Ding semistable Fano manifold $X$ satisfies that the anti-canonical volume is less than or equal to the value $(n+1)^n$. Moreover, the equality holds if and… Expand
On the K-stability of Fano varieties and anticanonical divisors
We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of… Expand
Simple normal crossing Fano varieties and log Fano manifolds
- K. Fujita
- Mathematics
- 10 June 2012
A projective log variety (X, D) is called "a log Fano manifold" if X is smooth and if D is a reduced simple normal crossing divisor on X with -(K_X+D) ample. The n-dimensional log Fano manifolds (X,… Expand
K-stability of Fano manifolds with not small alpha invariants
- K. Fujita
- Mathematics
- 27 June 2016
We show that any $n$-dimensional Fano manifold $X$ with $\alpha(X)=n/(n+1)$ and $n\geq 2$ is K-stable, where $\alpha(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$… Expand
Uniform K-stability and plt blowups of log Fano pairs
- K. Fujita
- Mathematics
- 1 January 2017
We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order… Expand
Examples of K-unstable Fano manifolds with the Picard number one
- K. Fujita
- Physics, Mathematics
- 18 August 2015
We show that the pair $(X, -K_X)$ is K-unstable for a del Pezzo manifold $X$ of degree five with dimension four or five. This disprove a conjecture of Odaka and Okada.
Classification of log del Pezzo surfaces of index three
- K. Fujita, Kazunori Yasutake
- Mathematics
- 7 January 2014
A normal projective non-Gorenstein log-terminal surface $S$ is called a log del Pezzo surface of index three if the three-times of the anti-canonical divisor $-3K_S$ is an ample Cartier divisor. We… Expand
Fano manifolds having (n-1,0)-type extremal rays with large Picard number
- K. Fujita
- Mathematics
- 20 December 2012
We classify smooth Fano manifolds X with the Picard number $\rho_X \geq 3$ such that there exists an extremal ray which has a birational contraction that maps a divisor to a point.
K-stability of log Fano hyperplane arrangements
- K. Fujita
- Mathematics
- 24 September 2017
In this article, we completely determine which log Fano hyperplane arrangements are uniformly K-stable, K-stable, K-polystable, K-semistable or not.