Discriminant loci of ample and spanned line bundles

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Let $(X,L,V)$ be a triplet where $X$ is an irreducible smooth complex projective variety, $L$ is an ample and spanned line bundle on $X$ and $V\subseteq H^0(X,L)$ spans $L$. The discriminant locus $\Cal D(X,V) \subset |V|$ is the algebraic subset of singular elements of $|V|$. We study the components of $\Cal D(X,V)$ in connection with the jumping sets of $(X,V)$, generalizing the classical biduality theorem. We also deal with the degree of the discriminant (codegree of $(X,L,V)$) giving some bounds on it and classifying curves and surfaces of codegree 2 and 3. We exclude the possibility for the codegree to be 1. Significant examples are provided.

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Analysis of PDEs, Algebraic Geometry, 14C20; 14N05

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http://salesiana.dossiersoluciones.com/handle/123456789/122993

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701870
 http://arxiv.org/abs/math/0701870

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arXiv