Deformations of product-quotient surfaces and reconstruction of Todorov surfaces via $\mathbb{Q}$-Gorenstein smoothing

Details Deformations of product-quotient surfaces and reconstruction of Todorov surfaces via $\mathbb{Q}$-Gorenstein smoothing Deformations of product-quotient surfaces and reconstruction of Todorov surfaces via $\mathbb{Q}$-Gorenstein smoothing

2012-01-24

arxiv.org/abs/1201.4925v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

We consider the deformation spaces of some singular product-quotient surfaces
$X=(C_1 \times C_2)/G$, where the curves $C_i$ have genus 3 and the group $G$
is either $\mathbb{Z}_2$ or $\mathbb{Z}_4$. As a by-product, we give a new
construction of Todorov surfaces with $p_g=1$, $q=0$ and $2\le K^2\le 8$ by
using $\mathbb{Q}$-Gorenstein smoothings techniques.

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