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Brill-Noether loci of divisors on irregular varieties
Rita Pardini (Università di Pisa) I will report on recent joint work with Margarida Mendes Lopes and Gian Pietro Pirola. Given a nonnegative integer r, a smooth projective variety X and a line bundle L on X one considers the r-th Brill-Noether locus W r(L,X), namely the set of line bundles P∈ Pic0(X) such that h0(L⊗ P)>r. When X is a surface without irrational pencils and L is effective, we introduce a Brill-Noether number and prove an existence theorem for W r(L,X) analogous to the classical one for linear series on smooth projective curves. As an application, we derive numerical inequalities for curves that do not move linearly on irregular surfaces. | ![]() |
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