RT Journal Article
T1 On the geometry of moduli spaces of coherent systems on algebraic curves.
A1 Bradlow, S.B.
A1 García Prada, O.
A1 Mercat, V.
A1 Muñoz, Vicente
A1 Newstead, P. E.
AB Let C be an algebraic curve of genus g ≥ 2. A coherent system on C consists of a pair (E, V ), where E is an algebraic vector bundle over C of rank n and degree d and V is a subspace of dimension k of the space of sections of E. The stability of the coherent system depends on a parameter a. We study the geometry of the moduli space of coherent systems for different values of a when k ≤ n and thevariation of the moduli spaces when we vary a. As a consequence, for sufficiently large , we compute the Picard groups and the first and second homotopy groupsof the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case k = n − 1 explicitly, and give the Poincare polynomials for thecase k = n − 2. In an appendix, we describe the geometry of the “flips” which takeplace at critical values of a in the simplest case, and include a proof of the existenceof universal families of coherent systems when GCD(n, d, k)= 1.
PB World Scientific
SN 0129-167X
YR 2007
FD 2007
LK https://hdl.handle.net/20.500.14352/50593
UL https://hdl.handle.net/20.500.14352/50593
LA eng
NO EAGER
NO EDGE
NO European Scientific Exchange Programme (Royal Society of London )
NO Consejo Superior de Investigaciones Científicas
NO National Science Foundation
DS Docta Complutense
RD 9 abr 2025