Smoothings of Fano varieties with normal crossing singularities

Abstract

This paper obtains criteria for a Fano variety X with normal crossing singularities defined over an algebraically closed field of characteristic zero, to be smoothable. The difference with the original version is that the theory of logarithmic structures and deformations is used in order to prove 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.

arXiv comment19 pages. Final version. To appear in the Proceedings of the Edinburgh Mathematical Society