What is the Jacobian of a Riemann surface with boundary?

2006/10/15 by Thomas M. Fiore, Igor Kriz, Igor Kříž +2
Mathematics · Physics and Astronomy · #14H40 #18C10 #32G15 (Secondary) #81T40 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #math-ph #math.AG #math.MP #msc:14H40 #msc:18C10 #msc:32G15 #msc:81T40

paper · pdf · doi:10.48550/arxiv.math/0610463

27 pages. Minor explanation and motivation added.

openalex publication_date 2006/10/15 · arxiv created 2008/06/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of ``open abelian varieties'' which satisfies gluing axioms similar to those of Riemann surfaces, and therefore allows a notion of ``conformal field theory'' to be defined on this space. We further prove that chiral conformal field theories corresponding to even lattices factor through this moduli space of open abelian varieties.

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