Brill–Noether loci on moduli spaces of symplectic bundles over curves
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Bajravani, Ali [1] ; Hitching, George H. [2]
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[1] Department of Mathematics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, P.O. Box: 53751-71379, Tabriz, Islamic Republic of Iran
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[2] Oslo Metropolitan University, Postboks 4, St. Olavs plass, 0130, Oslo, Norway
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 2, 2021, págs. 443-469
- Idioma: inglés
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Resumen
The symplectic Brill–Noether locus {{{\mathcal {S}}}}_{2n, K}^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 {{{\mathcal {S}}}}_{2n, K}^k. We show the nonemptiness of several {{{\mathcal {S}}}}_{2n, K}^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 B^k_{2n, 2n(g-1)} over any curve of genus g \ge 122. We obtain similar results for moduli spaces of coherent systems.
