N-Point Deformation of Algebraic K3 Surfaces

TL;DR

This paper explores N-point deformations of algebraic K3 surfaces, constructing explicit deformation moduli spaces and extending known two-point deformation methods to the general N-point case, revealing a dimension formula.

Contribution

It introduces a method to construct N-point deformations of algebraic K3 surfaces and derives the dimension of their moduli spaces, generalizing previous two-point deformation results.

Findings

Two-point deformation moduli space has dimension 19.

Extended to N-point case with moduli space dimension 19N(N-1)/2.

Method provides a framework for noncommutative deformations of K3 surfaces.

Abstract

We consider N-point deformation of algebraic K3 surfaces. First, we construct two-point deformation of algebraic K3 surfaces by considering algebraic deformation of a pair of commutative algebraic K3 surfaces. In this case, the moduli space of the noncommutative deformations is of dimension 19, the same as the moduli dimension of the complex deformations of commutative algebraic K3 surfaces. Then, we extend this method to the N-point case. In the N-point case, the dimension of deformation moduli space becomes 19N(N-1)/2.