The Szegö Kernel on a Sewn Riemann Surface
Tuite, Michael P.
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Michael P. Tuite and Alexander Zuevsky(2010)The Szegö Kernel on a Sewn Riemann Surface, Michael P. Tuite and Alexander Zuevsky
We describe the Szegö kernel on a higher genus Riemann surface in terms of Szegö 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 Szegö 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 Szegö kernel in these cases.