13 citations · 37 across the 9 of their papers we have counts for
9 papers
Localization of Atiyah classes
Marco Abate, Filippo Bracci, Tatsuo Suwa +1
We construct Atiyah classes using debar-closed forms. Under this point of view and using the Cech-Dolbeault cohomology, we provide several types of results about vanishing and loca…
Poincaré-Bendixson theorems for meromorphic connections and homogeneous vector fields
Marco Abate, Francesca Tovena
We first study the dynamics of the geodesic flow of a meromorphic connection on a Riemann surface, and prove a Poincaré-Bendixson theorem describing recurrence properties and -l…
Embeddings of submanifolds and normal bundles
Marco Abate, Filippo Bracci, Francesca Tovena
This paper is devoted to the study of the embeddings of a complex submanifold inside a larger complex manifold ; in particular, we are interested in comparing the embedding…
Index theorems for holomorphic maps and foliations
Marco Abate, Filippo Bracci, Francesca Tovena
We describe a general construction providing index theorems localizing the Chern classes of the normal bundle of a subvariety inside a complex manifold. As particular instances of…
Index theorems for holomorphic self-maps
Marco Abate, Filippo Bracci, Francesca Tovena
Let be a complex manifold and a (possibly singular) subvariety of . Let be a holomorphic map such that restricted to is the identity. W…
Formal normal forms for holomorphic maps tangent to the identity
Marco Abate, Francesca Tovena
We describe a procedure for constructing formal normal forms of holomorphic maps with a hypersurface of fixed points, and we apply it to obtain a complete list of formal normal for…