N-Point Deformation of Algebraic 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.