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1. CMB Online first
Note on the Grothendieck Group of Subspaces of Rational Functions and Shokurov's Cartier b-divisors 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 b-divisor, Grothendieck group Categories:14C20, 14Exx |
2. CMB 2001 (vol 44 pp. 452)
Some Adjunction Properties of Ample Vector Bundles Let $\ce$ be an ample vector bundle of rank $r$ on a projective
variety $X$ with only log-terminal singularities. We consider the
nefness of adjoint divisors $K_X + (t-r) \det \ce$ 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)
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 |