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Deformation of F-purity and F-regularity | | Anurag K. Singh
; | | Date: |
19 Sep 2002 | | Journal: | Journal of Pure and Applied Algebra {f 140} (1999) 137--148 | | Subject: | Commutative Algebra MSC-class: 13A35; 13B40; 13C20; 13H10 | math.AC | | Abstract: | 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)t^2 + ..., 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 S_3 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. | | Source: | arXiv, math.AC/0209241 | | Services: | Forum | Review | PDF | Favorites | |
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