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On the geometry of moduli spaces of coherent systems on algebraic curves.

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Bradlow, S.B. and García Prada, O. and Mercat, V. and Muñoz, Vicente and Newstead, P. E. (2007) On the geometry of moduli spaces of coherent systems on algebraic curves. International journal of mathematics, 18 (4). pp. 411-453. ISSN 0129-167X

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0129167X07004151


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Abstract

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 the
variation 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 groups
of 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 the
case k = n − 2. In an appendix, we describe the geometry of the “flips” which take
place at critical values of a in the simplest case, and include a proof of the existence
of universal families of coherent systems when GCD(n, d, k)= 1.


Item Type:Article
Uncontrolled Keywords:Algebraic curves; Moduli of vector bundles; Coherent systems; Brill–Noether loci
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21040
Deposited On:24 Apr 2013 14:14
Last Modified:12 Dec 2018 15:13

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