Number of moduli of ireducible families of plane curves with nodes and cusps.
Number of singular points of an annulus in
Using BMY inequality and a Milnor number bound we prove that any algebraic annulus in with no self-intersections can have at most three cuspidal singularities.
On a characterization of an abelian variety in the classification theory of algebraic varieties
On a Geometric Interpretation of Multiplicity.
On a local property of good frames in Thom-Boardman singularities
On a Result of Riemenschneider.
On Almost Complete Intersections.
On an infinitesimal invariant of normal.
On Auslander Modules of Normal Surface Singularities.
On Bertini's theorem.
On blowing up versal discriminants
It is well-known that the versal deformations of nonsimple singularities depend on moduli. The first step in deeper understanding of this phenomenon is to determine the versal discriminant, which roughly speaking is an obstacle for analytic triviality of an unfolding or deformation along the moduli. The goal of this paper is to describe the versal discriminant of and singularities basing on the fact that the deformations of these singularities may be obtained as blowing ups of certain deformations...
On branches at infinity of a pencil of polynomials in two complex variables
Let F ∈ ℂ[x,y]. Some theorems on the dependence of branches at infinity of the pencil of polynomials f(x,y) - λ, λ ∈ ℂ, on the parameter λ are given.
On Certain Numbers Associated to Isolated Critical Points.
On equimultiple subschemes of a local scheme over a field of characteristic zero
On equivalences of derived and singular categories
Let X and Y be two smooth Deligne-Mumford stacks and consider a pair of functions f: X → , g:Y → . Assuming that there exists a complex of sheaves on X × Y which induces an equivalence of D b(X) and D b(Y), we show that there is also an equivalence of the singular derived categories of the fibers f −1(0) and g −1(0). We apply this statement in the setting of McKay correspondence, and generalize a theorem of Orlov on the derived category of a Calabi-Yau hypersurface in a weighted projective...
On families of trajectories of an analytic gradient vector field
For an analytic function f:ℝⁿ,0 → ℝ,0 having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation ẋ = ∇f(x) attracted by the origin, given by characteristic exponents and asymptotic critical values.
On graded Bett numbers and geometrical properties of projective varieties.
On hypersurface singularities which are stems
On infinitesimal deformations of rational surface singularities
On Isolated Gorenstein Singularities.