A gluing construction of projective K3 surfaces

TL;DR

This paper presents a novel construction of a non-Kummer projective K3 surface with compact Levi-flats by holomorphically patching two complex surfaces derived from blow-ups of the projective plane.

Contribution

It introduces a new gluing method to construct specific K3 surfaces with Levi-flat structures, expanding the understanding of their complex geometry.

Findings

Constructed a non-Kummer projective K3 surface with Levi-flats.

Demonstrated holomorphic patching of complex surfaces from blow-ups.

Provided new examples of K3 surfaces with special geometric features.

Abstract

We construct a non-Kummer projective K3 surface $X$ which admits compact Levi-flats by holomorphically patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective plane at nine general points.