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

Ali Bajravani, George H. Hitching

• The symplectic Brill–Noether locus Sk2n,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 Sk2n,K. We show the nonemptiness of several Sk2n,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 Bk2n,2n(g−1) over any curve of genus g≥122. We obtain similar results for moduli spaces of coherent systems.