Injectivity of the symmetric map for line bundles

Details Injectivity of the symmetric map for line bundles Injectivity of the symmetric map for line bundles

2003-09-16

arxiv.org/abs/math/0309265v2

Mathematics

Algebraic Geometry

To appear in Manuscripta Mathematica. No changes in the paper. Word "generic" added to the abstract

Scientific paper

Let C be a generic non-singular curve of genus g defined over a field of
characteristic different from 2. We show that for every line bundle on C of
degree at most g+1, the natural product map S^2(H^0(L))\to H^0(C,L^2) is
injective. We also show that the bound on the degree of L is sharp.

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