Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Hamiltonian non-Kähler actions in low dimensions

Oliver Goertsches

created by bazzoni on 19 Feb 2021
modified on 19 Apr 2021

20 apr 2021 -- 16:00

Geometry in Como - Online

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We classify 3-valent GKM fiber bundles over n-gons, show that they are all realized as the projectivization of equivariant complex rank 2 vector bundles over quasitoric 4-manifolds, and investigate the existence of invariant (stable) almost complex, symplectic, and Kähler structures on the total space. In this way we obtain infinitely many new examples of Hamiltonian non-Kähler actions in dimension 6 with prescribed shape of the x-ray, in particular with prescribed number of fixed points. We extend our methods to give interesting examples of torus actions in dimension 8 that answer a natural cohomological rigidity question.

This is joint work with Panagiotis Konstantis and Leopold Zoller.

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