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Injectivity of the symmetric map for line bundles

Montserrat Teixidor i Bigas
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Abstract

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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Montserrat Teixidor i Bigas. 2003-09-17. Injectivity of the symmetric map for line bundles. https://arxiv.org/abs/math/0309265

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