7 papers
On the Equations Defining Toric L.C.I. Singularities
Dimitrios I. Dais, Martin Henk
Based on Nakajima's Classification Theorem we describe the precise form of the binomial equations which determine toric locally complete intersection ("l.c.i'') singularities.
Resolving 3-dimensional toric singularities
Dimitrios I. Dais
This paper surveys, in the first place, some basic facts from the classification theory of normal complex singularities, including details for the low dimensions 2 and 3. Next, it…
Crepant Resolutions of Gorenstein Toric Singularities and Upper Bound Theorem
Dimitrios I. Dais
A necessary condition for the existence of torus-equivariant crepant resolutions of Gorenstein toric singularities can be derived by making use of a variant of the classical Upper…
On the String-Theoretic Euler Number of a Class of Absolutely Isolated Singularities
Dimitrios I. Dais
An explicit computation of the so-called string-theoretic E-function of a normal complex variety X with at most log-terminal singularities can be achieved by constructing one snc-d…
On the String-Theoretic Euler Number of 3-dimensional A-D-E Singularities
Dimitrios I. Dais, Marko Roczen
The string-theoretic E-functions E_{str}(X;u,v) of normal complex varieties X having at most log-terminal singularities are defined by means of snc-resolutions. We give a direct co…
All toric l.c.i.-singularities admit projective crepant resolutions
Dimitrios I. Dais, Christian Haase, G"unter M. Ziegler
It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resol…