Vector Bundles Near Negative Curves: Moduli and Local Euler Characteristic |
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Authors: | E Ballico E Gasparim |
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Institution: | 1. Department of Mathematics , University of Trento , Povo , Trento , Italia;2. School of Mathematics, The University of Edinburgh , Edinburgh , Scotland , UK |
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Abstract: | We study moduli of vector bundles on a two-dimensional neighbourhood Z k of an irreducible curve ? ? ?1 with ?2 = ?k and give an explicit construction of their moduli stacks. For the case of instanton bundles, we stratify the stacks and construct moduli spaces. We give sharp bounds for the local holomorphic Euler characteristic of bundles on Z k and prove existence of families of bundles with prescribed numerical invariants. Our numerical calculations are performed using a Macaulay 2 algorithm, which is available for download at http://www.maths.ed.ac.uk/~s0571100/Instanton/. |
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Keywords: | Holomorphic vector bundles Local holomorphic Euler characteristic Local moduli |
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