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, B;Franciosi, M
;
Pardini, R
2022-01-01

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.
2022
Fantechi, B; Franciosi, M; Pardini, R
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/1154680
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 0
social impact