Let X be a smooth complex projective variety, let L be an ample line bundle on X spanned by a subspace V \subseteq H^0(X,L) defining a morphism phi:X \to P^N and let D(X,V) be its discriminant locus, i.e., the variety parameterizing the singular elements of |V|. We present two bounds on the dimension of D(X,V) and its main component relying on the geometry of phi(X) \subset P^N. Classification results for triplets (X,L,V) reaching the bounds as well as significant examples are provided.
Varieties with small discriminant variety / A. LANTERI, R. MUNOZ. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 358:12(2006), pp. 5565-5585.
Varieties with small discriminant variety
A. LANTERIPrimo
;
2006
Abstract
Let X be a smooth complex projective variety, let L be an ample line bundle on X spanned by a subspace V \subseteq H^0(X,L) defining a morphism phi:X \to P^N and let D(X,V) be its discriminant locus, i.e., the variety parameterizing the singular elements of |V|. We present two bounds on the dimension of D(X,V) and its main component relying on the geometry of phi(X) \subset P^N. Classification results for triplets (X,L,V) reaching the bounds as well as significant examples are provided.
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