IASM Preprint Series 2021-03: A noether-lefschetz theorem for spectral varieties with applications
XIAOYU SU AND BINWANG
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 k 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.