A canonical decomposition of generalized theta functions on the moduli stack of Gieseker vector bundles

dc.creatorKausz, Ivan
dc.date2003-05-01
dc.date2004-09-15
dc.date.accessioned2026-07-07T06:32:55Z
dc.date.available2026-07-07T06:32:55Z
dc.descriptionIn 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.description34 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.identifierhttps://arxiv.org/abs/math/0305034
dc.identifierhttp://arxiv.org/abs/math/0305034
dc.identifierJ. Algebraic Geom. 14 (2005), 439-480
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99021
dc.subjectAlgebraic Geometry
dc.subject14H60; 14F05
dc.titleA canonical decomposition of generalized theta functions on the moduli stack of Gieseker vector bundles
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