Prof. R. Parimala
Emory University, USA
November 23, 2022
Pencils of quadrics and hyperelliptic curves: Connections between the complex geometrry of a hyperelliptic curve $C$ and the internal geometry of the base locus of the associated pencil of quadrics are classical and trace back to Andre Weil. There is a rational description of of the moduli space of rank 2 stable bundles with odd determinant on a smooth hyperelliptic curve $C$ of genus $g$ in terms of the Grassmannian of $g-1$ dimensional linear subspaces contained in the base locus of the associated pencil of quadrics due to Ramanan. We explain a twist of this construction which leads to connections between period index bounds for the unramified Brauer classes on $K(C)$, $K$ being a totally imaginary number field and the existence of rational points on the Grasmannians in the associated pencil of quadrics.
Emory University, USA
November 23, 2022
Pencils of quadrics and hyperelliptic curves: Connections between the complex geometrry of a hyperelliptic curve $C$ and the internal geometry of the base locus of the associated pencil of quadrics are classical and trace back to Andre Weil. There is a rational description of of the moduli space of rank 2 stable bundles with odd determinant on a smooth hyperelliptic curve $C$ of genus $g$ in terms of the Grassmannian of $g-1$ dimensional linear subspaces contained in the base locus of the associated pencil of quadrics due to Ramanan. We explain a twist of this construction which leads to connections between period index bounds for the unramified Brauer classes on $K(C)$, $K$ being a totally imaginary number field and the existence of rational points on the Grasmannians in the associated pencil of quadrics.