A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds

Biswas, I and Pingali, VP (2018) A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds. In: Epijournal de Geometrie Algebrique, 2 .

PDF epi_geo_alg_2_2018.pdf - Published Version Restricted to Registered users only Download (450kB)

Abstract

A vector bundle on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. Nori proved that a vector bundle E on X is finite if and only if there is a finite étale Galois covering q : Xe −→ X and a Gal(q)-module V, such that E is isomorphic to the quotient of Xe × V by the twisted diagonal action of Gal(q) [No1], [No2]. Therefore, E is finite if and only if the pullback of E to some finite étale Galois covering of X is trivial. We prove the same statement when X is a compact complex manifold admitting a Gauduchon astheno-Kähler metric.

Item Type:	Journal Article
Publication:	Epijournal de Geometrie Algebrique
Publisher:	Association de l'Épijournal de Geometrie Algebrique
Additional Information:	The copyright for this article belongs to Association de l'Épijournal de Geometrie Algebriquethe author(s).
Keywords:	Astheno-Kähler manifolds; Finite bundles; Numerically flat bundles; Uhlenbeck-Yau theorem
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	14 Aug 2022 06:04
Last Modified:	14 Aug 2022 06:04
URI:	https://eprints.iisc.ac.in/id/eprint/75739

Actions (login required)

View Item