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The Szegő Kernel on a Sewn Riemann Surface

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Abstract

We describe the Szegő kernel on a higher genus Riemann surface in terms of Szegő kernel data coming from lower genus surfaces via two explicit sewing procedures where either two Riemann surfaces are sewn together or a handle is sewn to a Riemann surface. We consider in detail the examples of the Szegő kernel on a genus two Riemann surface formed by either sewing together two punctured tori or by sewing a twice-punctured torus to itself. We also consider the modular properties of the Szegő kernel in these cases.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland Galway, University Road, Galway, Ireland

    Michael P. Tuite & Alexander Zuevsky

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  1. Michael P. Tuite
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  2. Alexander Zuevsky
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Correspondence to Michael P. Tuite.

Additional information

Communicated by Y. Kawahigashi

Supported by a Science Foundation Ireland Research Frontiers Programme Grant, and by Max–Planck Institut für Mathematik, Bonn.

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Tuite, M.P., Zuevsky, A. The Szegő Kernel on a Sewn Riemann Surface. Commun. Math. Phys. 306, 617–645 (2011). https://doi.org/10.1007/s00220-011-1310-1

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  • DOI: https://doi.org/10.1007/s00220-011-1310-1

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