Singularities of non-$\mathbb{Q}$-Gorenstein varieties admitting a polarized endomorphism
Algebraic Geometry
2021-03-15 v6
Abstract
In this paper, we discuss a generalization of log canonical singularities in the non--Gorenstein setting. We prove that if a normal complex projective variety has a non-invertible polarized endomorphism, then it has log canonical singularities in our sense. As a corollary, we give an affirmative answer to a conjecture of Broustet and H\"{o}ring.
Cite
@article{arxiv.1811.01795,
title = {Singularities of non-$\mathbb{Q}$-Gorenstein varieties admitting a polarized endomorphism},
author = {Shou Yoshikawa},
journal= {arXiv preprint arXiv:1811.01795},
year = {2021}
}
Comments
21 pages. To appear in IMRN. This paper is revised about the following points that the assumption in Theorem 1.6 is removed, and Theorem 6.7, Definition 6.8 and Theorem 6.9 are added. Furthermore Section 7 is also added in version 4