Geodesic
Moduli space of principal sheaves over projective varieties
Tomás Gómez1 ; Ignacio Sols2
1 IMAFF - CSIC, Serrano 113 bis, 28006 Madrid, Spain
2 Departamento de Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense of Madrid, 28040 Madrid, Spain
Annals of mathematics, Tome 161 (2005) no. 2, pp. 1037-1092.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $E|_U$ and the vector bundle associated to $P$ by the adjoint representation.
DOI : 10.4007/annals.2005.161.1037

Tomás Gómez 1 ; Ignacio Sols 2

1 IMAFF - CSIC, Serrano 113 bis, 28006 Madrid, Spain
2 Departamento de Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense of Madrid, 28040 Madrid, Spain 
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Tomás Gómez; Ignacio Sols. Moduli space of principal sheaves over projective varieties. Annals of mathematics, Tome 161 (2005) no. 2, pp. 1037-1092. doi : 10.4007/annals.2005.161.1037. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.1037/

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