Seiberg-Witten invariants and surface singularities.
Semi-simple Carrousels and the Monodromy
Let be an open neighborhood of the origin in and let be complex analytic. Let be a generic linear form on . If the relative polar curve at the origin is irreducible and the intersection number is prime, then there are severe restrictions on the possible degree cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when is not prime.
Seshadri positive submanifolds of polarized manifolds
Let Y be a submanifold of dimension y of a polarized complex manifold (X, A) of dimension k ≥ 2, with 1 ≤ y ≤ k−1. We define and study two positivity conditions on Y in (X, A), called Seshadri A-bigness and (a stronger one) Seshadri A-ampleness. In this way we get a natural generalization of the theory initiated by Paoletti in [Paoletti R., Seshadri positive curves in a smooth projective 3-fold, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 1996, 6(4), 259–274] (which...
Shafarevich maps and plurigenera of algebraic varieties.
Simply-connected algebraic surfaces of positive index.
Simultaneous resolution of rational singularities
Simultaneous Resolution of Threefold Double Points.
Singularités à l’infini et intégration motivique
Soit un corps de caractéristique nulle et une fonction non constante définie sur une variété lisse. Nous définissons dans cet article unefibre de Milnor motivique à l’infiniqui appartient à un anneau de Grothendieck des variétés. Elle est définie en termes d’une compactification choisie, non nécessairement lisse, mais est indépendante de ce choix. Lorsque est le corps des nombres complexes, en utilisant le morphisme de réalisation de Hodge, elle se réalise en le spectre à l’infini de . Nous...
Singularités de Klein - I
Singularités de Klein - II
Singularités imposables en position générale à une hypersurface projective
Singularities and coverings of weighted complete intersections.
Singularities of polar curves
Skew fields of noncommutative rational functions (preliminary version)
-equivariant polynomial automorphisms of the binary forms
We consider the space of binary forms of degree denoted by . We will show that every polynomial automorphism of which commutes with the linear -action and which maps the variety of forms with pairwise distinct zeroes into itself, is a multiple of the identity on .
Small contractions of four dimensional algebraic manifolds.
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...
Smooth projective varieties dominated by smooth quadric hypersurfaces in any characteristic.
Smoothness, semi-stability and alterations
Solving the quintic by iteration in three dimensions.