TY - UNPB

T1 - Integral Picard group of the stack of quasi-polarized K3 surfaces of low degree

AU - Lorenzo, Andrea Di

N1 - 24 pages

PY - 2019/10/19

Y1 - 2019/10/19

N2 - We compute the integral Picard group of the stack $\mathcal{K}_{2l}$ of quasi-polarized K3 surfaces 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 $\mathcal{K}_{2l}$, in terms of the basis mentioned above.

AB - We compute the integral Picard group of the stack $\mathcal{K}_{2l}$ of quasi-polarized K3 surfaces 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 $\mathcal{K}_{2l}$, in terms of the basis mentioned above.

KW - math.AG

KW - 14J28, 14D23, 14C22, 14C15

M3 - Working paper

BT - Integral Picard group of the stack of quasi-polarized K3 surfaces of low degree

PB - ArXiv

ER -