<i>G</i>-invariant holomorphic Morse inequalities

Martin Puchol

doi:10.1016/j.crma.2015.12.010

Analytic geometry/Differential geometry

G-invariant holomorphic Morse inequalities

Presented by: the Editorial Board

Martin Puchol ¹

¹ Université Paris-Diderot – Paris-7, campus des Grands-Moulins, bâtiment Sophie-Germain, case 7012, 75205 Paris cedex 13, France

Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 526-531.

Abstract
Résumé

Consider an action of a connected compact Lie group on a compact complex manifold M, and two equivariant vector bundles L and E on M, with L of rank 1. In this note, we give holomorphic Morse inequalities in the spirit of Demailly for the invariant part of the Dolbeault cohomology of high tensor powers of L twisted by E, via the induced geometric data on the reduced space.

Considérons l'action d'un groupe de Lie compact connexe sur une variété complexe compacte, ainsi que deux fibrés vectoriels équivariants L et E sur M, avec L de rang 1. Dans cette note, nous donnons des inégalités de Morse dans l'esprit de Demailly pour la partie invariante de la cohomologie de Dolbeault des grandes puissances tensorielles de L tordues par E, en passant par les données géométriques induites sur l'espace réduit.

Received: 2015-05-21
Accepted: 2015-12-01
Published online: 2016-02-08

DOI: 10.1016/j.crma.2015.12.010

Author's affiliations:

Martin Puchol ¹

¹ Université Paris-Diderot – Paris-7, campus des Grands-Moulins, bâtiment Sophie-Germain, case 7012, 75205 Paris cedex 13, France

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     author = {Martin Puchol},
     title = {\protect\emph{G}-invariant holomorphic {Morse} inequalities},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {526--531},
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     doi = {10.1016/j.crma.2015.12.010},
     language = {en},
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Martin Puchol. G-invariant holomorphic Morse inequalities. Comptes Rendus. Mathématique, Volume 354 (2016) no. 5, pp. 526-531. doi : 10.1016/j.crma.2015.12.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.010/

References
Cited by

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