Regularized Integrals on Configuration Spaces of Riemann Surfaces and Cohomological Pairings
Algebraic Geometry
2026-01-16 v6 High Energy Physics - Theory
Mathematical Physics
Complex Variables
math.MP
Abstract
We extend the notion of regularized integrals introduced by Li-Zhou that aims to assign finite values to divergent integrals on configuration spaces of Riemann surfaces. We then give cohomological formulations for the extended notion using the tools of current cohomology and mixed Hodge structures. We also provide practical ways of constructing representatives of the corresponding cohomology classes in terms of smooth differential forms.
Keywords
Cite
@article{arxiv.2305.12362,
title = {Regularized Integrals on Configuration Spaces of Riemann Surfaces and Cohomological Pairings},
author = {Jie Zhou},
journal= {arXiv preprint arXiv:2305.12362},
year = {2026}
}
Comments
version 6: section 4 is rewritten to improve clarity, with a mistake corrected