Walls for Gieseker semistability and the Mumford-Thaddeus principle for moduli spaces of sheaves over higher dimensional bases
| dc.creator | Schmitt, Alexander | |
| dc.date | 1999-05-19 | |
| dc.date | 1999-05-23 | |
| dc.date.accessioned | 2026-07-07T05:29:07Z | |
| dc.date.available | 2026-07-07T05:29:07Z | |
| dc.description | Let $X$ be a complex projective manifold. Fix two ample line bundles $H_0$ and $H_1$ on $X$. It is the aim of this note to study the variation of the moduli spaces of Gieseker semistable sheaves for polarizations lying in the cone spanned by $H_0$ and $H_1$. We attempt a new definition of walls which naturally describes the behaviour of Gieseker semistability. By means of an example, we establish the possibility of non-rational walls which is a substantially new phenomenon compared to the surface case. Using the approach of Ellingsrud and Goettsche via parabolic sheaves, we were able to show that the moduli spaces undergo a sequence of GIT flips while passing a rational wall. | |
| dc.description | 10pp, AmSLaTeX (a4paper); Revised Version (some typos removed, Ex.1.1.5 completed) | |
| dc.identifier | https://arxiv.org/abs/math/9905110 | |
| dc.identifier | http://arxiv.org/abs/math/9905110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78519 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Walls for Gieseker semistability and the Mumford-Thaddeus principle for moduli spaces of sheaves over higher dimensional bases | |
| dc.type | text |