Families of K3 surfaces
Richard E. Borcherds, Ludmil Katzarkov, Tony Pantev, and N. I., Shepherd-Barron
TL;DR
This paper proves that a compact family of Kaehler K3 surfaces with constant Picard number is isotrivial using automorphic forms, contributing to the understanding of the moduli of K3 surfaces.
Contribution
It introduces a novel application of automorphic forms to establish isotriviality in families of K3 surfaces with fixed Picard number.
Findings
Proves isotriviality of certain K3 surface families
Demonstrates the use of automorphic forms in complex geometry
Advances understanding of K3 surface moduli
Abstract
We use automorphic forms to prove that a compact family of Kaehler K3 surfaces with constant Picard number is isotrivial.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric and Algebraic Topology