Symplectic and Kähler structures on CP1-bundles over CP2

TY - JOUR

T1 - Symplectic and Kähler structures on CP1-bundles over CP2

AU - Lindsay, Nicholas

AU - Panov, Dmitri

N1 - Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/11

Y1 - 2021/11

N2 - We show that there exist symplectic structures on a CP1-bundle over CP2 2 that do3 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

AB - We show that there exist symplectic structures on a CP1-bundle over CP2 2 that do3 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

UR - http://www.scopus.com/inward/record.url?scp=85116009641&partnerID=8YFLogxK

U2 - 10.1007/s00029-021-00705-7

DO - 10.1007/s00029-021-00705-7

M3 - Article

AN - SCOPUS:85116009641

SN - 1022-1824

VL - 27

JO - Selecta Mathematica

JF - Selecta Mathematica

IS - 5

M1 - 93

ER -