On Nakayama's Theorem

J. Math. Sci. Univ. Tokyo
Vol. 28 (2021), No. 4, Page 641-650.

Fujino, Osamu
On Nakayama's Theorem
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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.

Keywords: Negativity lemma, exceptional divisors, reflexive sheaves.

Mathematics Subject Classification (2010): Primary 14C20; Secondary 14E30.
Received: 2021-01-19