What is the Jacobian of a Riemann Surface with Boundary?

  • Thomas M. Fiore
  • Igor Kriz


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.


Modulus Space Riemann Surface Boundary Component Abelian Variety Mapping Class Group 


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© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2010

Authors and Affiliations

  • Thomas M. Fiore
  • Igor Kriz

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