Families of lattice polarized K3 surfaces with monodromy

Abstract

We extend the notion of lattice polarization for K3 surfaces to families over a (not necessarily simply connected) base, in a way that gives control over the action of monodromy on the algebraic cycles, and discuss the uses of this new theory in the study of families of K3 surfaces admitting fibrewise symplectic automorphisms. We then give an application of these ideas to the study of Calabi-Yau threefolds admitting fibrations by lattice polarized K3 surfaces.

References in corpus (6)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Lattice polarized toric K3 surfaces
• Some monodromy groups of finite index in $S{p}_4(\mathbb{Z})$
• Picard-Fuchs Differential Equations for Families of K3 Surfaces
• The 14th case VHS via K3 fibrations
• Moduli Stacks of Polarized K3 Surfaces in Mixed Characteristic

Cited by in corpus (8)

• Supersymmetric partition functions on Riemann surfaces
• Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
• The 14th case VHS via K3 fibrations
• Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves
• Hodge Numbers from Picard-Fuchs Equations
• Threefolds Fibred by Mirror Sextic Double Planes
• The Mirror Clemens-Schmid Sequence
• Normal Forms and Tyurin Degenerations of K3 Surfaces Polarised by a Rank 18 Lattice