Article ID Journal Published Year Pages File Type
4587416 Journal of Algebra 2009 23 Pages PDF
Abstract

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 2(a+b+c)>abc, a negative curve exists. Using a computer, we shall show that there exist examples in which this sufficient condition is not satisfied.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory