Deformed Hyperk\"{a}hler Structure for K3 Surfaces

TL;DR

This paper explores algebraic deformations of K3 surfaces, revealing a new deformed hyperk"{a}hler structure with a moduli space of dimension 57, significantly larger than classical deformations.

Contribution

It introduces a novel noncommutative deformation method for K3 surfaces, resulting in a deformed hyperk"{a}hler structure and an expanded moduli space.

Findings

Deformation moduli space has dimension 57.

Deformed triplet exhibits hyperk"{a}hler structure.

Moduli space dimension is three times that of classical deformations.

Abstract

We apply the method of algebraic deformation to N-tuple of algebraic K3 surfaces. When N=3, we show that the deformed triplet of algebraic K3 surfaces exhibits a deformed hyperk\"{a}hler structure. The deformation moduli space of this family of noncommutatively deformed K3 surfaces turns out to be of dimension 57, which is three times of that of complex deformations of algebraic K3 surfaces.