Deformations of product-quotient surfaces and reconstruction of Todorov surfaces via Q-Gorenstein smoothing

Abstract

We consider the deformation spaces of some singular product-quotient surfaces X = (C-1 x C-2)/G, where the curves C-i have genus 3 and the group G is isomorphic to Z(4). As a by-product, we give a new construction of Todorov surfaces with p(g) = 1, q = 0 and 2 <= K-2 <= 8 by using Q-Gorenstein smoothings.