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A note on exceptional unimodal singularities and K3 surfaces
exceptional unimodal singularities K3 surfaces note Algebraic Geometry
2011/9/1
Abstract: This is a short note on the relation between the graded stable derived categories of 14 exceptional unimodal singularities and the derived category of K3 surfaces obtained as compactificatio...
DB singularities deform
Du Bois singularities DB singularities deformation log canonical singularities non-lc ideal
2011/9/5
Abstract: Let $X$ be a variety and $H$ a Cartier divisor on $X$. We prove that if $H$ has Du Bois (or DB) singularities, then $X$ has Du Bois singularities near $H$. As a consequence, if $X \to S$ is ...
On Rees algebras and invariants for singularities over perfect fields
Rees algebras Integral closure Singularities Commutative Algebra
2011/8/31
Abstract: This purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations i...
Poincare series for plane curve singularities and their behaviour under projections
Curve singularity Alexander polynomial Poincare series value semigroup Grothendieck ring of varieties
2011/8/26
Abstract: Our purpose is to investigate all defined Poincar\'e series associated with multi-index filtrations and value semigroups of curve singularities---not necessarily complex---with regard to the...
An elliptic problem with two singularities
elliptic problem two singularities Analysis of PDEs
2011/8/26
Abstract: We study a Dirichlet problem for an elliptic equation defined by a degenerate coercive operator and a singular right-hand side. We will show that the right-hand side has some regularizing ef...
On isolated log canonical singularities with index one
log canonical singularities Cohen–Macaulay minimal model program mixed Hodge structures
2011/8/24
Abstract: In this paper, we give a method to investigate isolated log canonical singularities with index one which are not log terminal. Our method depends on the minimal model program. One of the mai...
Formation of singularities in solutions to ideal hydrodynamics of freely cooling inelastic gases
Formation of singularities hydrodynamics freely cooling inelastic gases
2011/8/23
Abstract: We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions ge...
Torsion and cotorsion in the sheaf of Kähler differentials on some mild singularities
Torsion cotorsion sheaf of Kä hler differentials some mild singularities
2011/3/1
We give a criterion for the sheaf of Kähler differentials on a cone over a smooth projective variety to be torsionfree.
Gorenstein isolated quotient singularities over C
Gorenstein isolated quotient singularities
2011/1/21
In this paper we review the classification of isolated quotient singularities over the field of complex numbers due to H. Zassenhaus,G. Vincent, and J. A. Wolf. As an application we describe Gorenstei...
Analytic classification of singularities in the generalized Kowalevski case
интегрируемые гамильтоновы системы отображение момента
2011/3/3
В задаче о движении волчка Ковалевской в двойном поле (случай интегрируемости А. Г. Реймана–М.А. Семенова-Тян-Шанского) вычислен тип всех критических точек отображения момента.
Analytic classification of singularities in the generalized Kowalevski case
слова интегрируемые гамильтоновы системы отображение момента
2010/12/28
В задаче о движении волчка Ковалевской в двойном поле (случай интегрируемости А. Г. Реймана–М.А. Семенова-Тян-Шанского) вычислен тип всех критических точек отображения момента.
A Geometric Representation of Improper Indefinite Affine Spheres with Singularities
Improper affine spheres Area distances Affine symmetry sets
2011/1/20
We consider in this paper a class of improper indefinite affine spheres with singularities in R3 called indefinite improper affine maps.We propose a representation of surfaces in this class by a pair ...
Tilting and cluster tilting for quotient singularities
Cohen-Macaulay module quotient singularity stable category triangulated category
2011/3/1
We shall show that the stable categories of graded Cohen-Macaulay modules over quotient
singularities have tilting objects. In particular, these categories are triangle equivalent to derived cat-egor...
Recent Progress on Singularities of Lagrangian Mean Curvature Flow
Recent Progress Singularities of Lagrangian Mean Curvature Flow
2011/1/20
We survey some of the state of the art regarding singu-larities in Lagrangian mean curvature
ow. Some open problems are suggested at the end.
On eigenvalues of differential equations with singularities, discontinuity conditions and turning points
eigenvalues of differential equations singularities turning points
2010/9/20
We consider the Sturm-Liouville equation on the bounded interval with two singularities in end points. This equation contains one turning point together with discontinuity conditions, moreover the tur...