The Szeg\"o Kernel on a Sewn Riemann Surface
Quantum Algebra
2020-12-14 v2 High Energy Physics - Theory
Complex Variables
Abstract
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.
Cite
@article{arxiv.1002.4114,
title = {The Szeg\"o Kernel on a Sewn Riemann Surface},
author = {Michael P. Tuite and Alexander Zuevsky},
journal= {arXiv preprint arXiv:1002.4114},
year = {2020}
}
Comments
Minor typos corrected, 37 pages, 3 figures. To appear in Commun. Math. Phys