Can I read Integral Picard group of some stacks of polarized K3 surfaces of low degree on EtoBox?

Integral Picard group of some stacks of polarized K3 surfaces of low degree by Di Lorenzo, Andrea is a scholarly article available to read on EtoBox.

What is Integral Picard group of some stacks of polarized K3 surfaces of low degree about?

We compute the integral Picard group of the stack $\mathcal{M}_{2l}$ of polarized K3 surfaces with at most rational double points of degree $2l=4,6,8$. We show that in this range the integral Picard group is torsion-free and that a basis is given by certain elliptic Noether-Lefschetz divisors together with the Hodge line bundle. To achieve this result, we investigate certain stacks of complete intersections and their Picard groups by means of equivariant geometry. In the end we compute an expression of the class of some Noether-Lefschetz divisors, restricted to an open substack of $\mathcal{M}_{2l}$, in terms of the basis mentioned above.

Author

Di Lorenzo, Andrea

Published

2019

Language

EN