RT Journal Article
T1 Torelli theorem for the moduli spaces of pairs
A1 Muñoz, Vicente
AB Let X be a smooth projective curve of genus g >= 2 over C. A pair (E, phi) over X consists of an algebraic vector bundle E over X and a section phi is an element of H(0)(E). There is a concept of stability for pairs which depends on a real parameter tau. Here we prove that the third cohomology groups of the moduli spaces of tau-stable pairs with fixed determinant and rank n >= 2 are polarised pure Hodge structures, and they are isomorphic to H(1) (X) with its natural polarisation (except in very few exceptional cases). This implies a Torelli theorem for such moduli spaces. We recover that the third cohomology group of the moduli space of stable bundles of rank n >= 2 and fixed determinant is a polarised pure Hodge structure, which is isomorphic to H(1) (X). We also prove Torelli theorems for the corresponding moduli spaces of pairs and bundles with non-fixed determinant.
PB Cambridge Univ Press
SN 0305-0041
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/50181
UL https://hdl.handle.net/20.500.14352/50181
LA eng
NO MEC
DS Docta Complutense
RD 9 abr 2025