On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 Surfaces

2015/11/04 by Bouyer, Florian · 1 citation
#14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.01299

Abstract

In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general (ℤ/2ℤ)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 (ℤ/2ℤ)⁴-invariant quartic K3 surface with a marked conic has 10 irreducible components.

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• Galois Groups of Symmetric Cubic Surfaces

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