Algebraic logarithmic deformations and applications to smoothings of Fano varieties with normal crossing singularities

Details Algebraic logarithmic deformations and applications to smoothings of Fano varieties with normal crossing singularities Algebraic logarithmic deformations and applications to smoothings of Fano varieties with normal crossing singularities

2010-05-04

arxiv.org/abs/1005.0531v1

Mathematics

Algebraic Geometry

24 pages.

Scientific paper

In this paper we first develop, following Kawamata and Namikawa, a logarithmic deformation theory for algebraic varieties over any field k and then we obtain criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. In particular, we show that X is smoothable by a smooth variety, if and only if T^1(X)=O_D, where D is the singular locus of X.

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