Symplectic and Kähler structures on CP1-bundles over CP2

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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
Original languageEnglish
Article number93
Number of pages24
JournalSelecta Mathematica
Issue number5
Early online date29 Sept 2021
Publication statusPublished - Nov 2021


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