Using the Zariski-van Kampen method, the fundamental group of the regular locus is ℤ⊕ℤ for the complexified planar Kepler problem and ℤ for the complexified spherical pendulum.
Hyperkaehler and holomorphic symplectic geometry
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abstract
We prove that all complex analytic subvarieties of a generic compact hyperkaehler manifold are even-dimensional. Moreover, these subvarieties are holomorphically symplectic.
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math.DS 1years
2023 1verdicts
UNVERDICTED 1representative citing papers
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A Remark on the Topology of the Regular Loci of Some Complexified Hamiltonian Systems
Using the Zariski-van Kampen method, the fundamental group of the regular locus is ℤ⊕ℤ for the complexified planar Kepler problem and ℤ for the complexified spherical pendulum.