Some necessary and sufficient condition for finite generation of symbolic Rees rings
Commutative Algebra
2022-12-13 v3 Algebraic Geometry
Abstract
Consider the blow-up Y of a weighted projective plane at a point in the open orbit over a field of characteristic 0. We assume that there exists a curve C on Y such that C^2<0 and C.E=1, where E is the exceptional curve. In this paper we give a (very simple) necessary and sufficient condition for finite generation of the Cox ring of Y (Theorem~1.2). It is an affirmative answer to a conjecture due to He and Kurano-Nishida.
Keywords
Cite
@article{arxiv.2204.01889,
title = {Some necessary and sufficient condition for finite generation of symbolic Rees rings},
author = {Taro Inagawa and Kazuhiko Kurano},
journal= {arXiv preprint arXiv:2204.01889},
year = {2022}
}
Comments
There were some typo in the previous version