A canonical decomposition of generalized theta functions on the moduli stack of Gieseker vector bundles
| dc.creator | Kausz, Ivan | |
| dc.date | 2003-05-01 | |
| dc.date | 2004-09-15 | |
| dc.date.accessioned | 2026-07-07T06:32:55Z | |
| dc.date.available | 2026-07-07T06:32:55Z | |
| dc.description | In this paper I present a new geometric approach to the factorization rule for generalised theta functions. Let $X$ be an irreducible projective nodal curve with one singularity and let $Y$ be its normalization. Recently I have constructed the moduli stack $GVB(X)$ of rank $n$ Gieseker vector bundles on $X$ and have shown that its normalization is a locally trivial fibration over the moduli stack $VB(Y)$ of vector bundles on $Y$, where the fibre is a canonical compactification of $Gl_n$. In this paper I prove a canonical direct sum decomposition of the space of global sections of a power of the theta line bundle on $GVB(X)$ where the summands are spaces of global sections of certain line bundles on the moduli stack of parabolic bundles on the two-pointed curve $Y$. | |
| dc.description | 34 pages. The old version has been thoroughly revised in order to enhance readability. In a new chapter I prove by explicit dimension count that the space of generalized theta functions behaves well under degeneration | |
| dc.identifier | https://arxiv.org/abs/math/0305034 | |
| dc.identifier | http://arxiv.org/abs/math/0305034 | |
| dc.identifier | J. Algebraic Geom. 14 (2005), 439-480 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99021 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H60; 14F05 | |
| dc.title | A canonical decomposition of generalized theta functions on the moduli stack of Gieseker vector bundles | |
| dc.type | text |