Determinants of pseudo-laplacians and $\zeta^{({\rm reg})}(1)$ for spinor bundles over Riemann surfaces

Abstract

Let $P$ be a point of a Riemann surface $X$. We study self-adjoint extensions of Dolbeault Laplacians in hermitian line bundles $L$ over $X$ initially defined on sections with compact supports in $X\backslash\{P\}$. We define the $\zeta$-regularized determinants for these operators and derive the comparison formulas for them. We introduce the notion of the Robin mass of $L$. This quantity enters the comparison formulas for determinants and is related to the regularized $\zeta(1)$ for the Dolbeault Laplacian. For spinor bundles of even characteristic, we find the explicit expressions for the Robin mass.

Locations

• arXiv (Cornell University) - View - PDF