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ndltd-NEU--neu-cj82n577h2021-05-27T05:11:13ZTwo explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.In Part I we study the moduli space of holomorphic parabolic vector bundles over a curve, using combinatorial techniques to obtain information about the structure of the cohomology ring. We consider the ring generated by the Chern classes of tautological line bundles on the moduli space of parabolic bundles of arbitrary rank on a Riemann surface. We show the Poincaré duals to these Chern classes have simple geometric representatives, and use this construction to show that the ring generated by these Chern classes vanishes below the dimension of the moduli space, in analogy with the Newstead-Ramanan conjecture for stable bundles.http://hdl.handle.net/2047/D20211399
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In Part I we study the moduli space of holomorphic parabolic vector bundles over a curve, using combinatorial techniques to obtain information about the structure of the cohomology ring. We consider the ring generated by the Chern classes of tautological line bundles on the moduli space of parabolic bundles of arbitrary rank on a Riemann surface. We show the Poincaré duals to these Chern classes have simple geometric representatives, and use this construction to show that
the ring generated by these Chern classes vanishes below the dimension of the moduli space, in analogy with the Newstead-Ramanan conjecture for stable bundles.
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| title |
Two explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.
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| spellingShingle |
Two explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.
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| title_short |
Two explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.
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| title_full |
Two explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.
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| title_fullStr |
Two explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.
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| title_full_unstemmed |
Two explorations in symplectic geometry: I. moduli spaces of parabolic vector bundles over curves II. characters of quantisations of Hamiltonian actions of compact Lie groups on symplectic manifolds.
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| title_sort |
two explorations in symplectic geometry: i. moduli spaces of parabolic vector bundles over curves ii. characters of quantisations of hamiltonian actions of compact lie groups on symplectic manifolds.
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http://hdl.handle.net/2047/D20211399
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1719407128753471488
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