2002/09/18 by Anurag K. Singh · 1 citation
Mathematics · #math.AC #msc:13A35 #msc:13B40 #msc:13C20 #msc:13H10
published as Journal of Pure and Applied Algebra {\bf 140} (1999) 137--148
arxiv created 2002/09/18 · arxiv updated 2009/11/30
Hochster and Huneke showed that the property of F-regularity deforms for Gorenstein rings, i.e., if (R,m) is a Gorenstein local ring such that R/tR is F-regular for some nonzerodivisor t in m, then R is F-regular. This result was later extended to the case of Q-Gorenstein rings by Smith (for rings of characteristic zero) and Aberbach, Katzman, and MacCrimmon (for rings of positive characteristic). We investigate the deformation of strong F-regularity using an anti-canonical cover of R, i.e., a symbolic Rees algebra S = R + It + I^(2)t2 + ..., where I is an inverse for the canonical module in the divisor class group of the ring R. We show that strong F-regularity deforms in the case that the symbolic powers I^(i) satisfy the Serre condition S3 for all i > 0, and the ring S is Noetherian. We also construct examples which show that the property of F-purity does not deform.