We construct the Atiyah classes of holomorphic vector bundles using (1, 0)-connections and developing a Chern-Weil type theory, allowing us to effectively compare Chern and Atiyah forms. Combining this point of view with the Cech-Dolbeault cohomology, we prove several results about vanishing and localization of Atiyah classes, and give some applications. In particular, we prove a Bott type vanishing theorem for (not necessarily involutive) holomorphic distributions. As an example we also present an explicit computation of the residue of a singular distribution on the normal bundle of an invariant submanifold that arises from the Camacho-Sad type localization.

Abate, M., Bracci, F., Suwa, T., Tovena, F. (2013). Localization of Atiyah classes. REVISTA MATEMATICA IBEROAMERICANA, 29(2), 547-578 [10.4171/RMI/730].

Localization of Atiyah classes

BRACCI, FILIPPO;TOVENA, FRANCESCA
2013-01-01

Abstract

We construct the Atiyah classes of holomorphic vector bundles using (1, 0)-connections and developing a Chern-Weil type theory, allowing us to effectively compare Chern and Atiyah forms. Combining this point of view with the Cech-Dolbeault cohomology, we prove several results about vanishing and localization of Atiyah classes, and give some applications. In particular, we prove a Bott type vanishing theorem for (not necessarily involutive) holomorphic distributions. As an example we also present an explicit computation of the residue of a singular distribution on the normal bundle of an invariant submanifold that arises from the Camacho-Sad type localization.
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Atiyah forms and classes; connections of type (1,0); Cech-Dolbeault cohomology; localization and residues; Bott type vanishing; singular holomorphic distributions
http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=29&iss=2&rank=6
Abate, M., Bracci, F., Suwa, T., Tovena, F. (2013). Localization of Atiyah classes. REVISTA MATEMATICA IBEROAMERICANA, 29(2), 547-578 [10.4171/RMI/730].
Abate, M; Bracci, F; Suwa, T; Tovena, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/88570
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