Smoothings of Fano schemes with normal crossing singularities of dimension at most three
arXiv:0907.3641
Abstract
We study the deformation theory of a Fano variety X with normal crossing singularities of dimension at most three. We obtain a formula for the sheaf T^1(X) of first order deformations of X in a suitable log resolution of X and its singular locus Z and we obtain explicit criteria for the existence of smoothings of X.
22 pages