マツオカ　ナオユキ   MATSUOKA Naoyuki   松岡　直之    所属   明治大学  理工学部    職種   専任教授
言語種別	英語
発行・発表の年月	2009/11
形態種別	学術雑誌
査読	査読あり
標題	On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves
執筆形態	共著(その他)
掲載誌名	Journal of Algebra
掲載区分	国外
巻・号・頁	322,pp.3268-3290
著者・共著者	Kazuhiko Kurano, Naoyuki Matsuoka
概要	In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal of the space monomial curves (ta, tb, tc) for pairwise coprime integers a, b, c such that (a, b, c) ≠ (1, 1, 1). If such a ring is not finitely generated over a base field, then it is a counterexample to the Hilbert's fourteenth problem. Finite generation of such rings is deeply related to existence of negative curves on certain normal projective surfaces. We study a sufficient condition (Definition 3.6) for existence of a negative curve. Using it, we prove that, in the case of (a + b + c)2>a b c, a negative curve exists. Using a computer, we shall show that there exist examples in which this sufficient condition is not satisfied. © 2008 Elsevier Inc. All rights reserved.
DOI	10.1016/j.jalgebra.2008.08.015
ISSN	00218693
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