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-X(1) := epsilon(l)(xt) (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(2)w = 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(X)1 for a semi-smooth variety X in terms of the gluing data.

Deformations of semi-smooth varieties / Fantechi, Barbara; Franciosi, Marco; Pardini, Rita. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - (2022), pp. 1-30. [10.1093/imrn/rnac261]

Deformations of semi-smooth varieties

Fantechi, Barbara;
2022

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-X(1) := epsilon(l)(xt) (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(2)w = 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(X)1 for a semi-smooth variety X in terms of the gluing data.
1
30
10.1093/imrn/rnac261
https://arxiv.org/abs/2010.02296
Fantechi, Barbara; Franciosi, Marco; Pardini, Rita
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/129850
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