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Deformations of semi-smooth varieties and the boundary of the moduli space of Godeaux surfaces

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EMG - New equivariant methods in algebraic and differential geometry

A variety X is semismooth if étale locally it is isomorphic to a product of a pinch point (x^2y-z2) with some affine space; equivalently, its normalization is smooth and X is obtained by gluing a smooth divisor to itself via an involution with fixed points in codimension 1. In joint work with Marco Franciosi and Rita Pardini, we calculate the sheaves T1_X and T_X in terms of the normalization and the gluing, and use this to show that all semi-smooth non normal stable Godeaux surfaces are smoothable, and nonsingular points of the moduli space. 

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