Deformation of F-purity and F-regularity
| dc.creator | Singh, Anurag K. | |
| dc.date | 2002-09-18 | |
| dc.date.accessioned | 2026-07-07T04:51:01Z | |
| dc.date.available | 2026-07-07T04:51:01Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0209241 | |
| dc.identifier | http://arxiv.org/abs/math/0209241 | |
| dc.identifier | Journal of Pure and Applied Algebra {\bf 140} (1999) 137--148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64999 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35; 13B40; 13C20; 13H10 | |
| dc.title | Deformation of F-purity and F-regularity | |
| dc.type | text |