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arXiv · 2204.01889

Some necessary and sufficient condition for finite generation of symbolic Rees rings

Taro Inagawa·Kazuhiko Kurano
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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.

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Taro Inagawa, Kazuhiko Kurano. 2022-04-04. Some necessary and sufficient condition for finite generation of symbolic Rees rings. https://arxiv.org/abs/2204.01889

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