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Moduli space of principal sheaves over projective varieties

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Sols, Ignacio and Gómez, Tomás L. (2005) Moduli space of principal sheaves over projective varieties. Annals of Mathematics, 161 (2). pp. 1037-1092. ISSN 0003-486X

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Official URL: http://0-annals.math.princeton.edu.cisne.sim.ucm.es/wp-content/uploads/annals-v161-n2-p11.pdf




Abstract

Let G be a connected reductive group. The late Ramanathan gave a notion of (semi)stable principal G-bundle on a Riemann surface and constructed a projective moduli space of such objects. We generalize Ramanathan's notion and construction to higher dimension, allowing also objects which we call semistable principal G-sheaves, in order to obtain a projective moduli space: a principal G-sheaf on a projective variety X is a triple (P, E, psi), where E is a torsion free sheaf on X, P is a principal G-bundle on the open set U where E is locally free and psi is an isomorphism between E vertical bar(U) and the vector bundle associated to P by the adjoint representation.


Item Type:Article
Uncontrolled Keywords:Compact riemann surface; Unitary vector bundles; Algebraic-curves
Subjects:Sciences > Mathematics > Algebra
ID Code:20368
Deposited On:13 Mar 2013 16:27
Last Modified:03 Oct 2018 14:02

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