Singularities of 2theta-divisors in the Jacobian

Details Singularities of 2theta-divisors in the Jacobian Singularities of 2theta-divisors in the Jacobian

1998-03-05

arxiv.org/abs/math/9803013v1

Mathematics

Algebraic Geometry

28 pages, Latex2e

Scientific paper

We study several subseries of the space of second order theta functions on the Jacobian of a non-hyperelliptic curve. In particular, we are interested in the subseries P\Gamma_{00} consisting of 2theta-divisors having multiplicity at least 4 at the origin, or, equivalently, containing the surface C-C, and in its analogues consisting of 2theta-divisors having higher multiplicities at the origin, containing the four-fold Sym^2C-Sym^2C, or singular along the surface C-C. We use rank 2 vector bundles with a given number of global sections to prove canonical isomorphisms between quotients of the above introduced subseries and vector spaces defined by the canonical divisor.

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