Injectivity of the symmetric map for line bundles
Montserrat Teixidor i Bigas
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 S2(H0(L)) H0(C,L2) is injective. We also show that the bound on the degree of L is sharp.
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