Smoothings of Schemes with Non-isolated Singularities

Smoothings of Fano Schemes with Normal Crossing Singularities of Dimension at Most Three

In this paper we study the deformation theory of a Fano variety X with normal crossing singularities. We obtain a formula for T (X) in a suitable log resolution of X and we obtain explicit criteria for the existence of smoothings of X.

The Signature of Smoothings of Higher Dimensional Singularities

Deformations of Q-calabi-yau 3-folds and Q-fano 3-folds of Fano Index 1

In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.

Rings of Singularities

This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...

Deformation Theory of Sandwiched Singularities

In this paper we describe the deformation theory of sandwiched sin-gularities in terms of-constant deformations of plane curves, and a divisor of points on it. This leads to an immediate understanding of the smoothings of sandwiched singularities in terms of pictures: certain conngurations of points and curves with only d-fold points in the plane. The topology of a smoothing can be described co...