Global Boundedness for Decorated Sheaves

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dc.creatorSchmitt, Alexander H. W.
dc.date2004-05-21
dc.date2004-08-03
dc.date.accessioned2026-07-07T05:08:27Z
dc.date.available2026-07-07T05:08:27Z
dc.descriptionAn important classification problem in Algebraic Geometry deals with pairs $(\E,ϕ)$, consisting of a torsion free sheaf $\E$ and a non-trivial homomorphism $ϕ\colon (\E^{\otimes a})^{\oplus b}\lra\det(\E)^{\otimes c}\otimes Ł$ on a polarized complex projective manifold $(X,Ø_X(1))$, the input data $a$, $b$, $c$, $Ł$ as well as the Hilbert polynomial of $\E$ being fixed. The solution to the classification problem consists of a family of moduli spaces ${\cal M}^δ:={\cal M}^{δ-\rm ss}_{a/b/c/L/P}$ for the $δ$-semistable objects, where $δ\in\Q[x]$ can be any positive polynomial of degree at most $\dim X-1$. In this note we show that there are only finitely many distinct moduli spaces among the ${\cal M}^δ$ and that they sit in a chain of "GIT-flips". This property has been known and proved by ad hoc arguments in several special cases. In our paper, we apply refined information on the instability flag to solve this problem. This strategy is inspired by the fundamental paper of Ramanan and Ramanathan on the instability flag.
dc.descriptionTo appear in the International Mathematics Research Notices. V2: A few typos corrected (notably in the definition of semistability in the introduction); Expanded Introduction
dc.identifierhttps://arxiv.org/abs/math/0405418
dc.identifierhttp://arxiv.org/abs/math/0405418
dc.identifierIMRN 2004:68 (2004) 3637-3671.
dc.identifierdoi:10.1155/S1073792804141652
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71273
dc.subjectAlgebraic Geometry
dc.titleGlobal Boundedness for Decorated Sheaves
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