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Brill–Noether loci on moduli spaces of symplectic bundles over curves

Hitching, George Harry; Bajravani, Ali
Journal article, Peer reviewed
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URI
https://hdl.handle.net/10642/9859
Date
2020-11-20
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  • LUI - Institutt for grunnskole- og faglærerutdanning [490]
Original version
Hitching, Bajravani. Brill–Noether loci on moduli spaces of symplectic bundles over curves. Collectanea Mathematica. 2020   https://doi.org/10.1007/s13348-020-00300-7
Abstract
The symplectic Brill–Noether locus Sk 2n,K associated to a curve C parametrises stable rank 2n bundles over C with at least k sections and which carry a nondegenerate skewsymmetric bilinear form with values in the canonical bundle. This is a symmetric determinantal variety whose tangent spaces are defined by a symmetrised Petri map. We obtain upper bounds on the dimensions of various components of Sk . We show the nonemptiness of several Sk , 2n,K 2n,K and in most of these cases also the existence of a component which is generically smooth and of the expected dimension. As an application, for certain values of n and k we exhibit components of excess dimension of the standard Brill–Noether locus Bk over any 2n,2n(g−1) curve of genus g ≥ 122. We obtain similar results for moduli spaces of coherent systems.
Publisher
Springer
Series
Collectanea Mathematica;
Journal
Collectanea Mathematica

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