A Noether-Lefschetz Theorem for Spectral Varieties with Applications
arXiv:2109.09989
Abstract
We calculate the Picard group of generic (very general) spectral varieties living in the total space of a very ample line bundle over an algebraically closed field of odd characteristics or characteristic 0. We follow the strategy of Ravindra and Srinivas [RS06,RS09] via formal Picard groups. As an application, we calculate the generic fibers of Hitchin systems over a smooth quintic surface of Picard number 1.
19 pages, on figure. Comments welcome!