Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on C and the comparison of different type of notions of stability arising in moduli theory. Notably we show that in certain cases these moduli spaces are birationally equivalent to fibrations over simple projective varieties, whose fibers are GIT quotients (ℙ r-1) rg//PGL(r), where r is the rank of the considered vector bundles. This allows us to compare different definitions of (semi-)stability (slope stability, α-stability, GIT stability) for vector bundles, coherent systems and point sets, and derive relations between them. In certain cases of vector bundles of low rank when C has small genus, our construction produces families of classical modular varieties contained in the Coble hypersurfaces

Bolognesi, M., Brivio, S. (2012). Coherent systems and modular subvarieties of SU_C(r). INTERNATIONAL JOURNAL OF MATHEMATICS, 23(4), 1-23 [10.1142/S0129167X12500371].

Coherent systems and modular subvarieties of SU_C(r).

BRIVIO, SONIA
Ultimo
2012

Abstract

Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on C and the comparison of different type of notions of stability arising in moduli theory. Notably we show that in certain cases these moduli spaces are birationally equivalent to fibrations over simple projective varieties, whose fibers are GIT quotients (ℙ r-1) rg//PGL(r), where r is the rank of the considered vector bundles. This allows us to compare different definitions of (semi-)stability (slope stability, α-stability, GIT stability) for vector bundles, coherent systems and point sets, and derive relations between them. In certain cases of vector bundles of low rank when C has small genus, our construction produces families of classical modular varieties contained in the Coble hypersurfaces
Articolo in rivista - Articolo scientifico
algebraic curves; Coble hypersurfaces; Moduli spaces of coherent systems; vector bundles
English
2012
23
4
1
23
1250037
open
Bolognesi, M., Brivio, S. (2012). Coherent systems and modular subvarieties of SU_C(r). INTERNATIONAL JOURNAL OF MATHEMATICS, 23(4), 1-23 [10.1142/S0129167X12500371].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/100384
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