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Transactions of the American Mathematical Society

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Varieties with small discriminant variety

Authors: Antonio Lanteri and Roberto Muñoz
Journal: Trans. Amer. Math. Soc. 358 (2006), 5565-5585
MSC (2000): Primary 14J40, 14N05, 14C20; Secondary 14F05, 14M99
Published electronically: July 20, 2006
MathSciNet review: 2238927
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Abstract: Let $ X$ be a smooth complex projective variety, let $ L$ be an ample and spanned line bundle on $ X$, $ V\subseteq H^{0}(X,L)$ defining a morphism $ \phi _{V}:X \to \mathbb{P}^{N}$ and let $ \mathcal{D}(X,V)$ be its discriminant locus, the variety parameterizing the singular elements of $ \vert V\vert$. We present two bounds on the dimension of $ \mathcal{D}(X,V)$ and its main component relying on the geometry of $ \phi _{V}(X) \subset \mathbb{P}^{N}$. Classification results for triplets $ (X,L,V)$ reaching the bounds as well as significant examples are provided.

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Additional Information

Antonio Lanteri
Affiliation: Dipartimento di Matematica “F. Enriques”, Università di Milano, Via C. Saldini 50, I-20133 Milano, Italy

Roberto Muñoz
Affiliation: Departamento de Matemáticas y Física aplicadas y Cc. de la Naturaleza, Universidad Rey juan Carlos, C. Tulipán, E-28933 Móstoles Madrid, Spain

Keywords: Complex projective variety, duality, defect, discriminant loci
Received by editor(s): February 17, 2004
Received by editor(s) in revised form: November 26, 2004
Published electronically: July 20, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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