Kulikov surfaces form a connected component of the moduli space

TL;DR

This paper proves that Kulikov surfaces constitute a connected component in the moduli space of surfaces with specific invariants, introduces a new description of these surfaces, and confirms they satisfy the Bloch conjecture.

Contribution

It establishes the connectedness of Kulikov surfaces in the moduli space and provides a new description extending Inoue's ideas.

Findings

Kulikov surfaces form a connected component in the moduli space.

A new description of Kulikov surfaces is provided.

Kulikov surfaces verify the Bloch conjecture.

Abstract

We show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type with p_g=0 and K^2=6. We also give a new description for the surfaces, extending ideas of Inoue. Finally we calculate the bicanonical degree of a Kulikov surface, and prove that they verify the Bloch conjecture.