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MATSUOKA Naoyuki
Department Undergraduate School , School of Science and Technology Position Professor |
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| Language | English |
| Publication Date | 2009/11 |
| Type | Academic Journal |
| Peer Review | Peer reviewed |
| Title | On finite generation of symbolic Rees rings of space monomial curves and existence of negative curves |
| Contribution Type | Co-authored (Other) |
| Journal | Journal of Algebra |
| Journal Type | Another Country |
| Volume, Issue, Page | 322,pp.3268-3290 |
| Author and coauthor | Kazuhiko Kurano, Naoyuki Matsuoka |
| Details | 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 |
| PermalinkURL | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70349378734&origin=inward |