Asymptotic regularity of powers of ideals of points in a weighted projective plane

Details Asymptotic regularity of powers of ideals of points in a weighted projective plane Asymptotic regularity of powers of ideals of points in a weighted projective plane

2009-10-22

arxiv.org/abs/0910.4232v1

Mathematics

Commutative Algebra

16 pages

Scientific paper

In this paper we study the asymptotic behavior of the regularity of symbolic powers of ideals of points in a weighted projective plane. By a result of Cutkosky, Ein and Lazarsfeld, regularity of such powers behaves asymptotically like a linear function. We study the difference between regularity of such powers and this linear function. Under some conditions, we prove that this difference is bounded, or eventually periodic. As a corollary we show that, if there exists a negative curve, then the regularity of symbolic powers of a monomial space curve is eventually a periodic linear function. We give a criterion for the validity of Nagata's conjecture in terms of the lack of existence of negative curves.

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