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arXiv · 0910.4232

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

Steven Dale Cutkosky·Kazuhiko Kurano
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Abstract

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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Steven Dale Cutkosky, Kazuhiko Kurano. 2009-10-22. Asymptotic regularity of powers of ideals of points in a weighted projective plane. https://doi.org/10.1215/0023608x-2010-019

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