Cohomology of toric bundles
Cohomology of toric bundles
复制标题
环面丛的上同调
DOI：
10.1007/s00014-003-0761-1
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发表时间：
2002
影响因子：
0.9
通讯作者：
V. Uma
中科院分区：
文献类型：
--
作者：
P. Sankaran;V. Uma
AbstractLet p:
AbstractLet p:
E → B
be a principal bundle with fibre and structure
group the torus T ≅ (
ℂ*)n over a
topological space B.
Let X be a nonsingular projective
T-toric variety.
One has the X-bundle
π : E(X)
→ B where
E(X)
= E ×TX,
π([e,x])
= p(e).
This is a Zariski locally trivial fibre bundle
in case p:
E →
B is algebraic. The purpose of this
note is to describe (i) the singular cohomology ring of
E(X)
as an H*
(B;ℤ)-algebra,
(ii) the topological K-ring of
K*
(E(X))
as a K*
(B)-algebra when
B is compact.
When p :
E →
B is algebraic over an irreducible,
nonsingular, noetherian scheme over
ℂ, we describe (iii) the Chow ring of
A*
(E(X))
as an A*
(B)-algebra, and
(iv) the Grothendieck ring $\mathcal K$0
(E
(X)) of algebraic vector
bundles on E
(X) as a
$\mathcal K$0(B)-algebra.