A Note on Equimultiple Deformations
| dc.creator | Markwig, Thomas | |
| dc.date | 2007-05-26 | |
| dc.date.accessioned | 2026-07-07T08:03:19Z | |
| dc.date.available | 2026-07-07T08:03:19Z | |
| dc.description | While the tangent space to an equisingular family of curves can be discribed by the sections of a twisted ideal sheaf, this is no longer true if we only prescribe the multiplicity which a singular point should have. However, it is still possible to compute the dimension of the tangent space with the aid of the equimulitplicity ideal. In this note we consider families L_m={(C,p) | mult_p(C)=m} with C in some linear system |L| on a smooth projective surface S and for a fixed positive integer m, and we compute the dimension of the tangent space to L_m at a point (C,p) depending on whether p is a unitangential singular point of C or not. We deduce that the expected dimension of L_m at (C,p) in any case is just dim|L|+2-m*(m+1)/2. The result is used in the study of triple-point defective surfaces in some joint papers with Luca Chiantini. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0705.3911 | |
| dc.identifier | http://arxiv.org/abs/0705.3911 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129540 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14B07; 32S15 | |
| dc.title | A Note on Equimultiple Deformations | |
| dc.type | text |