Classification of Picard lattices of K3 surfaces

TL;DR

This paper classifies Picard lattices of K3 surfaces based on their finite symplectic automorphism groups and rational curves, extending previous degeneration classifications.

Contribution

It provides a detailed classification of Picard lattices of K3 surfaces considering automorphism groups and rational curves, building on earlier degeneration results.

Findings

Classification of Picard lattices based on automorphism groups

Identification of rational curves in negative definite lattices

Extension of degeneration classification results

Abstract

Using results of our papers [19], [20] and [21] about classification of degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, we classify Picard lattices of Kahlerian K3 surfaces. By classification we understand classification depending on their possible finite symplectic automorphism groups and their non-singular rational curves if a Picard lattice is negative definite.