Yujiro Kawamata

Subadjunction of log canonical divisors, II

<abstract abstract-type=TeX><p>We extend a subadjunction formula of log canonical divisors as in [Kawamata, <i>Contemp. Math.</i><b>207</b> (1997), 79-88] to the case when the codimension of the minimal center is arbitrary by using the positivity of the Hodge bundles.

On Fujita's freeness conjecture for 3-folds and 4-folds

We shall prove a conjecture of T. Fujita on the freeness of the adjoint linear systems in some cases: Let X be a smooth projective variety of dimension n and H an ample divisor. Assume that n = 3 or 4. Then |KX + mH| is free if m ≥ n + 1. Moreover, we obtain more precise result in the case n = 3.

Deformations of canonical singularities

M. Reid defined the concept of canonical singularities as those which appear on canonical models of algebraic varieties whose canonical rings are finitely generated. From the view point of the classification theory of algebraic varieties, it is expected that small deformations of a variety which has only canonical singularities have only canonical singularities. The main result of this paper states that this is the case:

On the Cone of divisors of Calabi-Yau fiber spaces

We prove some version of Morrisons conjecture on the cone of divisors for Calabi-Yau fiber spaces with non-trivial base pace whose total space is 3-dimensional.

On a Relative Version of Fujita’s Freeness Conjecture

The following is Fujita’s freeness conjecture: Conjecture 1.1. Let X be a smooth projective variety of dimension n and H an ample divisor. Then the invertible sheaf Ox(K x + mH) is generated by global sections m≥n+1, or m=n and H n ≥2.