Moduli of Bundles in Low Genus, Coble Hypersurfaces and Degeneracy Loci

Explore the intricate connections between Coble hypersurfaces, Abelian varieties, and moduli of semistable bundles in this advanced mathematics lecture. Delve into the properties of Coble hypersurfaces and their relationship to moduli spaces of semistable bundles with trivial determinant on curves of genus 2 and 3. Examine the use of orbital degeneracy loci arising from Vinberg theta-groups and Hecke cycles to describe moduli of semistable bundles with fixed odd determinant as subvarieties of Grassmannians. Investigate the geometric parallels between these loci, their singularities, and Coble hypersurfaces, and discover their connections to projective models of K3 surfaces and the Hasset divisor of cubic fourfolds. Gain insights into this collaborative research conducted with Vladimiro Benedetti, Michele Bolognesi, and Laurent Manivel.