Existence of good divisors on Mukai varieties

Existence of good divisors on Mukai manifolds

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...

N 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...

Basic results on irregular varieties via Fourier--Mukai methods

Recently Fourier–Mukai methods have proved to be a valuable tool in the study of the geometry of irregular varieties. The purpose of this paper is to illustrate these ideas by revisiting some basic results. In particular, we show a simpler proof of the Chen–Hacon birational characterization of abelian varieties. We also provide a treatment, along the same lines, of previous work of Ein and Laza...

Some Basic Results on Irregular Varieties Revisited with the Fourier-mukai Transform

Recently Fourier-Mukai methods have proved to be a valuable tool in the study of the geometry of irregular varieties. An especially interesting point is the interplay between the generic vanishing theorems of Green and Lazarsfeld and the notion of generic vanishing sheaves, naturally arising in the Fourier-Mukai context. The purpose of this mainly expository paper is to exemplify this circle of...

THEOREMS ABOUT GOOD DIVISORS ON LOG FANO VARIETIES ( CASE OF INDEX r > n - 2 )