Log-terminal smoothings of graded normal surface singularities

Smoothings of Schemes with Non-isolated Singularities

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 deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced scheme of finite type over a field k to have smoothings and Q-Gorenstein smoothings.

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

Line Bundles Associated with Normal Surface Singularities

In [15] L. Nicolaescu and the author formulated a conjecture which relates the geometric genus of a complex analytic normal surface singularity (X, 0) (whose link M is a rational homology sphere) with the Seiberg-Witten invariant of M associated with the “canonical” spin structure of M . (The interested reader is invited to see the articles [15, 16, 17, 13, 19, 20] for the verification of the c...

Kawachi’s Invariant for Normal Surface Singularities

We study a useful numerical invariant of normal surface singularities, introduced recently by T. Kawachi. Using this invariant, we give a quick proof of the (well-known) fact that all log-canonical surface singularities are either elliptic Gorenstein or rational (without assuming a priori that they are Q -Gorenstein). In §2 we prove effective results (stated in terms of Kawachi’s invariant) reg...