Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4587416 | Journal of Algebra | 2009 | 23 Pages |
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