Let X be a smooth complex projective n-fold endowed with an ample and spanned line bundle L. Under the assumption that |L| defines a generically one-to-one map we describe the singular set and the general element in the main component of the discriminant locus of |L|. The description is used to show that (X,L) is covered by lienar P^k's, where k+1 stands for the codimension of the main component. We also give some applications relating k to the spectral value of (X,L) and discuss some examples.

Discriminant loci of varieties with smooth normalization / A. Lanteri, M. Palleschi, A.J. Sommese. - In: COMMUNICATIONS IN ALGEBRA. - ISSN 0092-7872. - 28:9(2000), pp. 4179-4200.

Discriminant loci of varieties with smooth normalization

A. Lanteri;M. Palleschi;
2000

Abstract

Let X be a smooth complex projective n-fold endowed with an ample and spanned line bundle L. Under the assumption that |L| defines a generically one-to-one map we describe the singular set and the general element in the main component of the discriminant locus of |L|. The description is used to show that (X,L) is covered by lienar P^k's, where k+1 stands for the codimension of the main component. We also give some applications relating k to the spectral value of (X,L) and discuss some examples.
Adjunction theory; Ample and spanned line bundle; Defect; Discriminant locus; Generically one-to-one morphism; Nondegenerate quadratic singularity
Settore MAT/03 - Geometria
COMMUNICATIONS IN ALGEBRA
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/178618
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