The Szegö Kernel on a Sewn Riemann Surface

Details The Szegö Kernel on a Sewn Riemann Surface The Szegö Kernel on a Sewn Riemann Surface

2010-02-22

arxiv.org/abs/1002.4114v2

Mathematics

Quantum Algebra

Minor typos corrected, 37 pages, 3 figures. To appear in Commun. Math. Phys

Scientific paper

We describe the Szeg\"o kernel on a higher genus Riemann surface in terms of Szeg\"o 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 Szeg\"o 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 Szeg\"o kernel in these cases.

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