Related papers: Classification of threefold enc cDV quotient singu…

We classify some special classes of non-rational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found.

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

This paper contains an account of arbitrary cubic function fields of characteristic three. We define a standard form for an arbitrary cubic curve and consider its function field. By considering an integral basis for the maximal order of…

In characteristic zero, quotient singularities are log terminal. Moreover, we can check whether a quotient variety is canonical or not by using only the age of each element of the relevant finite group if the group does not have…

We study solutions to conformally invariant equations with isolated singularties.

We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein…

In this paper we generalize standard results about non-commutative resolutions of quotient singularities for finite groups to arbitrary reductive groups. We show in particular that quotient singularities for reductive groups always have…

The purpose of this paper is to construct a crepant resolution of quotient singularities by trihedral groups ( finite subgroups of SL(3,C) of certain type ), and prove that each Euler number of the minimal model is equal to the number of…

This paper studies hypersurface exceptional singularities in $\mathbb C^n$ defined by non-degenerate function. For each canonical hypersurface singularity, there exists a weighted homogeneous singularity such that the former is exceptional…

We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of…

We give an overview of the existing algorithms to compute nonunique factorization invariants in finitely generated monoids.

We study complex spatial quartic surfaces with simple singularities up to equisingular deformations; as a first step, give a complete equisingular deformation classification of the so-called non-special simple quartic surfaces.

The paper presents an algorithm for topological classification of nondegenerate saddle-focus singularities of integrable Hamiltonian systems with three degrees of freedom up to semi-local equivalence. In particular, we prove that any…

Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.

For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic…

Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the…

We construct a family of 1-convex threefolds, with exceptional curve C of type (0,-2), which are not embeddable in C^m \times CP_n. In order to show that they are not Kaehler we exhibit a real 3-dimensional chain A whose boundary is the…

In this paper we give the classification of rank 3 vector bundles without "inner" cohomology on a quadric hypersurface \Q_n (n>3) by studying the associated monads.

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

We classify the possible ramification data and etale local structure of orders over surfaces with canonical singularities.