Deformations of semi-smooth varieties

2020/10/05 by Fantechi, Barbara, Franciosi, Marco, Pardini, Rita · 1 citation
#14D15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.02296

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 T¹_X:=ext¹(Omega_X,O_X). A variety is semi-smooth if its singularities are étale locally the product of a double crossing point (uv=0) or a pinch point (u²-v²w=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 T¹_X for a semi-smooth variety X in terms of the gluing data.

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