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On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 Surfaces (1511.01299v1)
Published 4 Nov 2015 in math.AG
Abstract: In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general $(\mathbb{Z}/2\mathbb{Z}){4}$-invariant quartic K3 surface contains at least $320$ conics. In this paper we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space $(\mathbb{Z}/2\mathbb{Z}){4}$-invariant quartic K3 surface with a marked conic has $10$ irreducible components.