A linear bound for Frobenius powers and an inclusion bound for tight closure
Commutative Algebra
2007-05-23 v2 Algebraic Geometry
Abstract
Let I denote an R_+ -primary homogeneous ideal in a normal standard-graded Cohen-Macaulay domain over a field of positive characteristic p. We give a linear degree bound for the Frobenius powers I^[q] of I, q=p^e, in terms of the minimal slope of the top-dimensional syzygy bundle on the projective variety Proj R. This provides an inclusion bound for tight closure. In the same manner we give a linear bound for the Castelnuovo-Mumford regularity of the Frobenius powers I^[q].
Keywords
Cite
@article{arxiv.math/0405463,
title = {A linear bound for Frobenius powers and an inclusion bound for tight closure},
author = {Holger Brenner},
journal= {arXiv preprint arXiv:math/0405463},
year = {2007}
}
Comments
Some minor changes and some examples added; to appear in Mich. Math. Journal