Existence of good divisors on Mukai manifolds
نویسنده
چکیده
A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety, indeed recently, Minimal Model Theory predicted that every uniruled variety is birational to a fiber space whose general fiber is a Fano variety with terminal singularities. The index of a Fano variety X is the number
منابع مشابه
Existence of good divisors on Mukai varieties
A normal projective variety X is called Fano if a multiple of the anticanonical Weil divisor, −KX , is an ample Cartier divisor. The importance of Fano varieties is twofold, from one side they give, has predicted by Fano [Fa], examples of non rational varieties having plurigenera and irregularity all zero (cfr [Is]); on the other hand they should be the building block of uniruled variety. Indee...
متن کاملMirror Symmetry and Self-dual Manifolds
We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-Kähler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the existence of a transformation similar to the Fourier-Mukai functor, suggest that this approach may be able to explain mirror symmetry also in other situations.
متن کاملFibrations, Divisors and Transcendental Leaves
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of fibrations, the topology of smooth hypersurfaces and the topological closure of transcendental leaves of foliations.
متن کاملN ov 2 00 3 Fourier - Mukai transforms between canonical divisors , and its application to describing Fourier - Mukai partners
Let X be a smooth 3-fold whose kodaira dimension is positive. The main purpose of this paper is to investigate the set of smooth projective varieties Y whose derived categories of coherent sheaves are equivalent to that of X as triangulated categories. If there exists an equivalence Φ: D(X)→ D(Y ) we can compare derived categories of canonical divisors of X and Y , and this gives an inductive t...
متن کاملNon existence of totally contact umbilical slant lightlike submanifolds of indefinite Sasakian manifolds
We prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite Sasakian manifolds other than totally contact geodesic proper slant lightlike submanifolds. We also prove that there do not exist totally contact umbilical proper slant lightlike submanifolds of indefinite Sasakian space forms.
متن کامل