Numerically Trivial Fibrations
نویسنده
چکیده
We develop an intersection theory for a singular hermitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure associated with the singular hermitian line bundle. Also for any pseudoeffective line bundle on a smooth projective variety, we prove the existence of a natural rational fibration structure associated with the line bundle. We also characterize a numerically trivial singular hermitain line bundle on a smooth projective variety. MSC32J25
منابع مشابه
The Gromov-witten and Donaldson-thomas Correspondence for Trivial Elliptic Fibrations
We study the Gromov-Witten and Donaldson-Thomas correspondence conjectured in [MNOP1, MNOP2] for trivial elliptic fibrations. In particular, we verify the Gromov-Witten and Donaldson-Thomas correspondence for primary fields when the threefold is E × S where E is a smooth elliptic curve and S is a smooth surface with numerically trivial canonical class.
متن کاملNumerically Trivial Foliations, Iitaka Fibrations and the Numerical Dimension
Modifying the notion of numerically trivial foliation of a pseudoeffective line bundle L introduced by the author in [Eck04a] (see also math.AG/0304312) it can be shown that the leaves of this foliation have codimension ≥ the numerical dimension of L as defined by Boucksom, Demailly, Paun and Peternell, math.AG/0405285. Furthermore, if the Kodaira dimension of L equals its numerical dimension t...
متن کاملBuilding a Model Category out of Cofibrations and Fibrations: the Two out of Three Property for Weak Equivalences
The purpose of this note is to understand the two out of three property of the model category in terms of the weak factorization systems. We will show that if a category with classes of trivial cofibrations, cofibrations, trivial fibrations, and fibrations is given a simplicial structure similar to that of the simplicial model category, then the full subcategory of cofibrant and fibrant objects...
متن کاملar X iv : 0 90 4 . 02 73 v 1 [ m at h . A G ] 1 A pr 2 00 9 Fibrations on four - folds with trivial canonical bundles ∗
Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.
متن کاملLocally Trivial Families of Hyperelliptic Curves: the Geometry of the Weierstrass Scheme Remke Kloosterman and Orsola Tommasi
In this paper we describe some geometrical properties of the Weierstrass scheme of locally trivial hyperelliptic fibrations.
متن کامل