On Nakayama's theorem

zbMATH Open1479.14013arXiv2101.00166MaRDI QIDQ5031215

Osamu Fujino

Publication date: 18 February 2022

Abstract: The main purpose of this paper is to make Nakayama's theorem more accessible. We give a proof of Nakayama's theorem based on the negative definiteness of intersection matrices of exceptional curves. In this paper, we treat Nakayama's theorem on algebraic varieties over any algebraically closed field of arbitrary characteristic although Nakayama's original statement is formulated for complex analytic spaces.

Full work available at URL: https://arxiv.org/abs/2101.00166

zbMATH Keywords

reflexive sheavesexceptional divisorsnegativity lemma

Mathematics Subject Classification ID

Minimal model program (Mori theory, extremal rays) (14E30) Divisors, linear systems, invertible sheaves (14C20)

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