Kulikov surfaces form a connected component of the moduli space

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 these surfaces, extending ideas of Inoue. Finally, we calculate the bicanonical degree of Kulikov surfaces and prove that they verify the Bloch conjecture.