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The Szegő kernel on a sewn Riemann surface. (English) Zbl 1238.30029
Authors’ 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.

MSC:
30F10 Compact Riemann surfaces and uniformization
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
17B69 Vertex operators; vertex operator algebras and related structures
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