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# George Hitching, Brill-Noether Loci on Moduli Space of Symplectic Bundles over a Curve

## September 6, 2023 @ 11:00 am - 12:00 pm KST

Let *C* be a smooth projective curve of genus *g*. The symplectic Brill-Noether locus *S*(*k*, 2*n*, *K*) parametrises stable bundles of rank 2*n* over *C* with at least *k* independent sections, and which admit a nondegenerate skewsymmetric bilinear form with values in the canonical bundle *K*. This is a symmetric determinantal variety whose tangent spaces are described by a symmetrised Petri map. We show for many values of *g*, *n* and *k* that *S*(*k*, 2*n*, *K*) is nonempty and has a component which is generically smooth and of the expected dimension. As an application, we show that for certain *n* and *k*, for any curve of large genus the usual Brill-Noether locus *B*(*k*, 2*n*, 2*n*(*g*-1)) has a component of excess dimension. This is joint work with Ali Bajravani (Tabriz/Berlin).