Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves |
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| Authors: | S B Bradlow O García-Prada V Mercat V Muñoz |
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| Institution: | 1. Department of Mathematics , University of Illinois , Urbana , Illinois , USA;2. Instituto de Ciencias Matemáticas CSIC-UAM-UCM-UC3M , Consejo Superior de Investigaciones Científicas , Madrid , Spain;3. rue Delouvain , Paris , France |
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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 α. We study the geometry of the moduli space of coherent systems for 0 < d ≤ 2n. We show that these spaces are irreducible whenever they are nonempty and obtain necessary and sufficient conditions for nonemptiness. |
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| Keywords: | Algebraic curves Brill–Noether loci Coherent systems Moduli of vector bundles |
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