ON THE MONODROMY AND GALOIS GROUP OF CONICS LYING ON HEISENBERG INVARIANT QUARTIC K3 SURFACES

In [5], Eklund showed that a general (DOUBLE-STRUCK CAPITAL Z/2DOUBLE-STRUCK CAPITAL 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 of (DOUBLE-STRUCK CAPITAL Z/2DOUBLE-STRUCK CAPITAL Z)(4)-invariant quartic K3 surface with a certain marked conic has 10 irreducible components.