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arXiv · 2010.02296

Deformations of semi-smooth varieties

Barbara Fantechi·Marco Franciosi·Rita Pardini
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Abstract

For a singular variety X, an essential step to determine its smoothability and study its deformations is the understanding of the tangent sheaf and of the sheaf T^1_X:=ext^1(Omega_X,O_X). A variety is semi-smooth if its singularities are \'etale locally the product of a double crossing point (uv=0) or a pinch point (u^2-v^2w=0) with affine space; equivalently, if it can be obtained by gluing a smooth variety along a smooth divisor via an involution with smooth quotient. Our main result is the explicit computation of the tangent sheaf and the sheaf T^1_X for a semi-smooth variety X in terms of the gluing data.

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Barbara Fantechi, Marco Franciosi, Rita Pardini. 2020-10-05. Deformations of semi-smooth varieties. https://arxiv.org/abs/2010.02296

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