Varieties with small discriminant variety
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- by Antonio Lanteri and Roberto Muñoz PDF
- Trans. Amer. Math. Soc. 358 (2006), 5565-5585 Request permission
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 $|V|$. 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.References
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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
- Email: lanteri@mat.unimi.it
- 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
- Email: roberto.munoz@urjc.es
- Received by editor(s): February 17, 2004
- Received by editor(s) in revised form: November 26, 2004
- Published electronically: July 20, 2006
- © Copyright 2006 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 5565-5585
- MSC (2000): Primary 14J40, 14N05, 14C20; Secondary 14F05, 14M99
- DOI: https://doi.org/10.1090/S0002-9947-06-03915-8
- MathSciNet review: 2238927