Related papers: Classification of toric surface singularities

We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or…

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

We give criteria for Morin singularities for germs of maps into lower dimensions. As an application, we study the bifurcation of Lefschetz singularities.

Toric subvarieties of projective space are classified up to projective automorphisms.

We characterize plane curve germes non-degenerate in Kouchnirenko's sense in terms of characteristics and intersection multiplicities of branches.

The object of this survey is to give an overview on the topology of singularities of holomorphic foliation germs on $(\mathbb C^2,0)$.

We consider log del Pezzo surfaces coming with a non-trivial torus action. Such a surface is 1/k-log canonical if it allows a resolution of singularities with discrepanies all greater or equal to 1/k-1. We provide a concrete classification…

In this paper we show that any hypersurface singularities of germs of varieties in positive characteristic can be resolved by iterated monoidal transformations in centers in smooth subvarieties, if we have a valuation ring of iterated…

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

We study the subvariety of singular sections, the discriminant, of a base point free linear system $|L|$ on a smooth toric variety $X$. On one hand we describe pairs $(X,L)$ for which the discriminant is of low dimension. Precisely, we…

We prove a conjecture of Shokurov which characterises toric varieties using log pairs.

We classify surjective self-maps (of degree at least two) of affine surfaces according to the log Kodaira dimension.

We describe a class of toric varieties in the $N$-dimensional affine space which are minimally defined by no less than $N-2$ binomial equations.

In this paper, we prove that two normal complex surface germs that are inner bilipschitz--but not necessarily orientation-preserving--homeomorphic, have in fact the same oriented topological type and the same minimal plumbing graph. Along…

Two subset germs of Euclidean spaces are called blow-spherically equivalent, if their spherical modifications are homeomorphic and the homeomorphism induces homeomorphic tangent links. Blow-spherical equivalence is stronger than the…

We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive…

In this notes we classify toric Fano 4-folds having positive second Chern Character.

We classify singular foliations admitting a given leaf and a given transverse singular foliation.

We study semi-stable degenerations of toric varieties determined by certain partitions of their moment polytopes. Analyzing their defining equations we prove a property of uniqueness.

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and…