Related papers: On a certain generalization of triangle singularit…
This paper gives upper bounds for the dimension of the singularity category of a Cohen-Macaulay local ring with an isolated singularity. One of them recovers an upper bound given by Ballard, Favero and Katzarkov in the case of a…
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.
It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and…
For a triangulated category A with a 2-periodic dg-enhancement and a triangulated oriented marked surface S we introduce a dg-category F(S,A) parametrizing systems of exact triangles in A labelled by triangles of S. Our main result is that…
We define homology groups for flat irregular singular connections on surfaces and a pairing between these and the de Rham cohomology of the connection, generalizing work of S. Bloch and H. Enault in dimension one. Assuming a conjecture of…
We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the…
A finite subgroup of ${\rm SL}_2(\CC)$ defines a (Kleinian) rational surface singularity. The McKay correspondence yields a relation between the Poincar\'e series of the algebra of invariants of such a group and the characteristic…
We study certain toric Gorenstein varieties with isolated singularities which are the quotient spaces of generic unimodular representations by the one-dimensional torus, or by the product of the one-dimensional torus with a finite abelian…
We study isolated quotient singularities by finite and linearly reductive group schemes (lrq singularities for short) and show that they satisfy many, but not all, of the known properties of finite quotient singularities in characteristic…
In the author's paper ''Poincar\'{e} series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity'' a relation is proved between the Poincar\'{e} series of the coordinate algebra of a two-dimensional quasihomogeneous…
In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for…
The 3-dimensional Heisenberg group can be equipped with three different types of left-invariant Lorentzian metric, according to whether the center of the Lie algebra is spacelike, timelike or null. Using the second of these types, we study…
We describe a relation between Arnold's strange duality and a polar duality between the Newton polytopes which is mostly due to M.~Kobayashi. We show that this relation continues to hold for the extension of Arnold's strange duality found…
This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the…
We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being…
We present a classification algorithm for isolated hypersurface singularities of corank 2 and modality 1 over the real numbers. For a singularity given by a polynomial over the rationals, the algorithm determines its right equivalence class…
In this paper we consider the symmetries of triangulable half-dilation structures on the sphere with four singularities. We show that all such surfaces can be produced by a tetrahedral construction. Using this construction, we calculate…
We study the relationship between singularity categories and relative singularity categories and discuss constructions of differential graded algebras of relative singularity categories. As consequences, we obtain structural results, which…
We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…
We show that the Zariski canonical stratification of complex hypersurfaces is locally bi-Lipschitz trivial along the strata of codimension two. More precisely, we study Zariski equisingular families of surface, not necessarily isolated,…