posted on 2024-07-03, 10:48authored byJoseph Prebble
We study families of K3 surfaces polarised by a particular rank 18 lattice composed of one copy of the hyperbolic lattice and two copies of the (unique) even negative definite unimodular lattice of rank 8. We determine the normal form of a threefold to which all such families are birational over a base. Singular fibres of these families then correspond to geometric conditions over the moduli space for such surfaces. We exhibit the families with central fibre set to be singular under various conditions and determine how one can arrive at different projective models for these families and thus attain different Tyurin degenerations.