Publication: On the geometry of moduli spaces of coherent systems on algebraic curves.
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Publication Date
2007
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World Scientific
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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.
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