Laplacians on fuzzy Riemann surfaces

Gluing formulas for determinants of Dolbeault laplacians on Riemann surfaces

We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary satisfying local elliptic boundary conditions. The conditions are defined using the additional structure of a framing, or trivialization of the bundle near the boundary. An application to the comp...

Computing on Riemann Surfaces

These notes are a review on computational methods that allow us to use computers as a tool in the research of Riemann surfaces, algebraic curves and Jacobian varieties. It is well known that compact Riemann surfaces, projective algebraiccurves and Jacobian varieties are only diierent views to the same object, i.e., these categories are equivalent. We want to be able to put our hands on this equ...

Coalescence on Riemann Surfaces

We consider coalescing fermions on a Riemann Surface and derive generalized determinant formulas, complementing some results of 3].

Tau-functions on spaces of holomorphic differentials over Riemann surfaces and determinants of Laplacians in flat metrics with conic singularities over Riemann surfaces

The main goal of this paper is to compute (up to a moduli-independent constant factor) determinants of Laplacians in flat metrics with conic singularities on compact Riemann surfaces. We consider two classes of metrics: the Ströbel metrics and metrics given by moduli square of a holomorphic differential. For the latter case, if all conic angles equal 4π, our formulas essentially coincide with h...

Determinants of Laplacians and an Isopolar Compactness Theorem for Riemann Surfaces of Infinite Area