1. CMB 2013 (vol 57 pp. 562)
 Kaveh, Kiumars; Khovanskii, A. G.

Note on the Grothendieck Group of Subspaces of Rational Functions and Shokurov's Cartier bdivisors
In a previous paper the authors developed an intersection theory for
subspaces of rational functions on an algebraic variety $X$
over $\mathbf{k} = \mathbb{C}$. In this short note, we first extend this intersection
theory to an arbitrary algebraically closed ground field $\mathbf{k}$.
Secondly we give an isomorphism between the group of Cartier
$b$divisors on the birational class of $X$
and the Grothendieck group
of the semigroup of subspaces of rational functions on $X$. The
constructed isomorphism moreover
preserves the intersection numbers. This provides an alternative point
of view on Cartier $b$divisors and their intersection theory.
Keywords:intersection number, Cartier divisor, Cartier bdivisor, Grothendieck group Categories:14C20, 14Exx 

2. CMB 2001 (vol 44 pp. 452)
 Ishihara, Hironobu

Some Adjunction Properties of Ample Vector Bundles
Let $\ce$ be an ample vector bundle of rank $r$ on a projective
variety $X$ with only logterminal singularities. We consider the
nefness of adjoint divisors $K_X + (tr) \det \ce$ when $t \ge \dim X$
and $t>r$. As an application, we classify pairs $(X,\ce)$ with
$c_r$sectional genus zero.
Keywords:ample vector bundle, adjunction, sectional genus Categories:14J60, 14C20, 14F05, 14J40 

3. CMB 1998 (vol 41 pp. 267)
 Fukuma, Yoshiaki

On the nonemptiness of the adjoint linear system of polarized manifold
Let $(X,L)$ be a polarized manifold over the complex number field
with $\dim X=n$. In this paper, we consider a conjecture of
M.~C.~Beltrametti and A.~J.~Sommese and we obtain that this
conjecture is true if $n=3$ and $h^{0}(L)\geq 2$, or $\dim \Bs
L\leq 0$ for any $n\geq 3$. Moreover we can generalize the
result of Sommese.
Keywords:Polarized manifold, adjoint bundle Categories:14C20, 14J99 
