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Smoothings of Fano schemes with normal crossing singularities of dimension at most three
Nikolaos Tziolas
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 deformati…
Smoothings of schemes with non-isolated singularities
Nikolaos Tziolas
In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformation…
3-fold divisorial extremal neighborhoods over cE7 and cE6 Compound DuVal singularities
Nikolaos Tziolas
Let X be the germ of a Gorenstein 3-fold singularity and C a smooth curve through it such that the general hyperplane section S of X containing D is DuVal of type E6 or E7. In this…
Q-Gorenstein deformations of non-normal surfaces
Nikolaos Tziolas
Revised Version. An example of a locally smoothable stable surface that does not have a global smoothing has been added.
Three dimensional divisorial extremal neighborhoods
Nikolaos Tziolas
Revised version. Proper credits added. In this paper we study divisorial extremal neighborhoods f:Y-->X, such that X is a cAn type three dimensional terminal singularity, and C=f(E…
Terminal 3-fold divisorial contractions of a surface to a curve, I
Nikolaos Tziolas
Let C be a smooth curve on an index 1 terminal 3-fold. We investigate the existence of extremal terminal divisorial contractions Y-->X that contract an irreducible surface E to C.…