What is the Jacobian of a Riemann surface with boundary?

Details What is the Jacobian of a Riemann surface with boundary? What is the Jacobian of a Riemann surface with boundary?

2006-10-15

arxiv.org/abs/math/0610463v3

Mathematics

Algebraic Geometry

27 pages. Minor explanation and motivation added.

Scientific paper

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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