Families of Lattice Polarized K3 Surfaces with Monodromy

2013/12/22 by Charles F. Doran, Andrew Harder, Andrey Novoseltsev +2
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Algebraic surface #Automorphism #Geometry and complex manifolds #K3 surface #Lattice (music) #Mathematical analysis #Mathematics #Monodromy #Physics #Pure mathematics #Symplectic geometry #math.AG #msc:14J32

paper · pdf · doi:10.1093/imrn/rnv071

published as Int. Math. Res. Notices (2015), No. 23, 12265-12318

arxiv created 2013/12/22 · openalex publication_date 2015/03/09 · arxiv updated 2016/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 three-folds admitting fibrations by lattice polarized K3 surfaces.

Citations

• Hodge Theory and Complex Algebraic Geometry II
• Moduli Stacks of Polarized K3 Surfaces in Mixed Characteristic
• Arithmetic triangle groups
• A TORELLI THEOREM FOR ALGEBRAIC SURFACES OF TYPEK3
• Compact Complex Surfaces