Carlo Perrone - Academia.edu (original) (raw)

Papers by Carlo Perrone

Publicacions Matematiques, Jul 1, 2011

We study some numerical properties of singularities of codimension one holomorphic foliations whi... more We study some numerical properties of singularities of codimension one holomorphic foliations which can be analytically collapsed to one point. Some local and global dynamical consequences are deduced.

Bulletin Des Sciences Mathematiques, 2010

We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n ,... more We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n , 0). We prove that the irreducible components with dimension comparable with the rank of W are of minimal degree.

Mathematische Annalen, Mar 12, 2009

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties ... more We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Aside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho-Sad type index theorem for holomorphic foliations of singular complex varieties.

Publicacions Matemàtiques, 2011

We study some numerical properties of singularities of codimension one holomorphic foliations whi... more We study some numerical properties of singularities of codimension one holomorphic foliations which can be analytically collapsed to one point. Some local and global dynamical consequences are deduced.

Mathematische Annalen, 2009

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties ... more We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Aside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho-Sad type index theorem for holomorphic foliations of singular complex varieties.

Bulletin des Sciences Mathématiques, 2010

We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n ,... more We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n , 0). We prove that the irreducible components with dimension comparable with the rank of W are of minimal degree.

Publicacions Matematiques, Jul 1, 2011

We study some numerical properties of singularities of codimension one holomorphic foliations whi... more We study some numerical properties of singularities of codimension one holomorphic foliations which can be analytically collapsed to one point. Some local and global dynamical consequences are deduced.

Bulletin Des Sciences Mathematiques, 2010

We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n ,... more We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n , 0). We prove that the irreducible components with dimension comparable with the rank of W are of minimal degree.

Mathematische Annalen, Mar 12, 2009

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties ... more We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Aside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho-Sad type index theorem for holomorphic foliations of singular complex varieties.

Publicacions Matemàtiques, 2011

We study some numerical properties of singularities of codimension one holomorphic foliations whi... more We study some numerical properties of singularities of codimension one holomorphic foliations which can be analytically collapsed to one point. Some local and global dynamical consequences are deduced.

Mathematische Annalen, 2009

We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties ... more We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Aside a study of the general properties of such a cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho-Sad type index theorem for holomorphic foliations of singular complex varieties.

Bulletin des Sciences Mathématiques, 2010

We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n ,... more We study the subvariety of integrable 1-forms in a finite dimensional vector space W ⊂ Ω 1 (C n , 0). We prove that the irreducible components with dimension comparable with the rank of W are of minimal degree.