Picard Groups on Moduli of K3 Surfaces with Mukai Models
نویسندگان
چکیده
We discuss the Picard group of the moduli space Kg of quasi-polarized K3 surfaces of genus g ≤ 12 and g 6= 11. In this range, Kg is unirational, and a general element in Kg is a complete intersection with respect to a vector bundle on a homogenous space, by the work of Mukai. In this paper, we find generators for the Picard group PicQ(Kg) using Noether-Lefschetz theory. This verifies the Noether-Lefschetz conjecture on the moduli of K3 surfaces in these cases.
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