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Publications Influence

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

66 11- PDF

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

76 10- PDF

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

14 2- PDF

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

32 2- PDF

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

32 2- PDF

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.

15 1- PDF

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

13 1- PDF

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.

8 1- PDF

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.

17 1- PDF