The Szegö Kernel on a Sewn Riemann Surface

Abstract

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.

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

References in corpus (3)

• Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
• Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
• On Genus Two Riemann Surfaces Formed from Sewn Tori

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• Reduction cohomology of Riemann surfaces