Viene presentata una costruzione che, dato un arbitrario nodo , produce allo stesso tempo: 1) un'applicazione polinomiale con singolarità (debolmente) isolata in e come tipo di nodo della singolarità; 2) una risoluzione delle singolarità di nel senso di Hironaka. Specializzando la costruzione ai nodi fibrati otteniamo una versione debole (a meno di scoppiementi e nella categoria analitica reale) di un reciproco per il teorema di fibrazione di Milnor.
In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.
We show that coefficients of residue formulas for characteristic numbers associated to a smooth toral action on a manifold can be taken in a quotient field This yields canonical identities over the integers and, reducing modulo two, residue formulas for Stiefel Whitney numbers.
For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is , a simple characterization of this geometrical property is proved.
We derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities . The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.
We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.
Given a cohomology class there is a smooth submanifold Poincaré dual to . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in . This note summarizes some results on the question: how does the divisibility of restrict the dual submanifolds in this class ? A formula for signatures associated with a -fold ramified cover of branched along is given and a proof is included in case .
The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
We investigate the knots in the boundary of the punctured complex projective plane. Our result gives an affirmative answer to a question raised by Suzuki. As an application, we answer to a question by Mathieu.
Two significant directions in the development of jet calculus are showed. First, jets are generalized to so-called quasijets. Second, jets of foliated and multifoliated manifold morphisms are presented. Although the paper has mainly a survey character, it also includes new results: jets modulo multifoliations are introduced and their relation to (R,S,Q)-jets is demonstrated.