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Symplectic and Kähler structures on CP1-bundles over CP2

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number93
Number of pages24
JournalSelecta Mathematica
Volume27
Issue number5
Early online date29 Sep 2021
DOIs
Accepted/In press19 Aug 2021
E-pub ahead of print29 Sep 2021
PublishedNov 2021

Bibliographical note

Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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Abstract

We show that there exist symplectic structures on a CP1-bundle over CP2 2 that do
3 not admit a compatible Kähler structure. These symplectic structures were originally constructed by Tolman and they have a Hamiltonian T2 4 -symmetry. Tolman’s manifold was shown to be diffeomorphic to a CP1-bundle over CP2 5 by Goertsches, Konstantis, 6 and Zoller. The proof of our result relies on Mori theory, and on classical facts about holomorphic vector bundles over CP2

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