A numerical criterion for simultaneous normalization
| dc.creator | Chiang-Hsieh, Hung-Jen | |
| dc.creator | Lipman, Joseph | |
| dc.date | 2004-08-28 | |
| dc.date | 2005-10-20 | |
| dc.date.accessioned | 2026-07-07T08:06:26Z | |
| dc.date.available | 2026-07-07T08:06:26Z | |
| dc.description | We investigate conditions for "simultaneous normalizability" of a family of reduced schemes, i.e., the normalization of the total space normalizes, fiber by fiber, each member of the family. The main result (under more general conditions) is that a flat family of reduced equidimensional projective complex varieties X_y with parameter y ranging over a normal space--algebraic or analytic--admits a simultaneous normalization if and only if the Hilbert polynomial of the integral closure of the structure sheaf O_{X_y} is locally independent of y. When the X_y are curves projectivity is not needed, and the statement reduces to the well known δ-constant criterion of Teissier. Proofs are basically algebraic, analytic results being related via standard techniques (Stein compacta, etc.) to more abstract algebraic ones. | |
| dc.description | 35 pages, final version. To appear in Duke Math. J | |
| dc.identifier | https://arxiv.org/abs/math/0408394 | |
| dc.identifier | http://arxiv.org/abs/math/0408394 | |
| dc.identifier | Duke Math. J. 133 (2006), 347-390. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130608 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14B05, 32S15 | |
| dc.title | A numerical criterion for simultaneous normalization | |
| dc.type | text |