Singularities II: Automorphisms of Forms.
Singularities of hyperdeterminants
We study the singular locus of the variety of degenerate hypermatrices of an arbitrary format. Our main result is a classification of irreducible components of the singular locus. Equivalently, we classify irreducible components of the singular locus for the projectively dual variety of a product of several projective spaces taken in the Segre embedding.
Singularities of nets of quadrics
Singularities of polar curves
Singularities of Quotients by Vector Fields in Characteristic p.
Singularities of the moduli spaces of certain abelian surfaces
Singularities on complete algebraic varieties
We prove that any finite set of n-dimensional isolated algebraic singularities can be afforded on a simply connected projective variety.
Singularities with exact Poincaré complex but not quasihomogeneous.
We give examples of complete intersections in C3 with exact Poincaré complex but not quasihomogeneous using the classification of C.T.C. and the algorithm of Mora.
Skew-Symmetric Vanishing Lattices and Their Monodromy Groups.
Skew-Symmetric Vanishing Lattices and Their Monodromy Groups. II.
Small Deformations of Normal Singularities.
Smooth double subvarieties on singular varieties, III
Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form , s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F is a (N-1)-fold...
Smoothness, semi-stability and alterations
Some consequences of perversity of vanishing cycles
For a holomorphic function on a complex manifold, we show that the vanishing cohomology of lower degree at a point is determined by that for the points near it, using the perversity of the vanishing cycle complex. We calculate this order of vanishing explicitly in the case the hypersurface has simple normal crossings outside the point. We also give some applications to the size of Jordan blocks for monodromy.
Some geometric aspects of Puiseux surfaces.
This paper is part of the author's thesis, recently presented, where the following problem is treated: Characterizing the tangent cone and the equimultiple locus of a Puiseux surface (that is, an algebroid embedded surface admitting an equation whose roots are Puiseux power series) , using a set of exponents appearing in a root of an equation. The aim is knowing to which extent the well known results for the quasi-ordinary case can be extended to this much wider family.
Some properties of double point schemes
Specialization of MacPherson's Chern classes.
Specialization of Segre classes of singular algebraic varieties.
Springer fiber components in the two columns case for types and are normal
We study the singularities of the irreducible components of the Springer fiber over a nilpotent element with in a Lie algebra of type or (the so-called two columns case). We use Frobenius splitting techniques to prove that these irreducible components are normal, Cohen–Macaulay, and have rational singularities.
Stratification theory from the Newton polyhedron point of view
Recently, T. Fukui and L. Paunescu introduced a weighted version of the -regularity condition and Kuo’s ratio test condition. In this approach, we consider the - regularity condition and -regularity related to a Newton filtration.