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1. CJM 2007 (vol 59 pp. 981)
The Chen--Ruan Cohomology of Weighted Projective Spaces In this paper we study the Chen--Ruan cohomology ring of weighted
projective spaces. Given a weighted projective space ${\bf
P}^{n}_{q_{0}, \dots, q_{n}}$, we determine all of its twisted
sectors and the corresponding degree shifting numbers. The main
result of this paper is that the obstruction bundle over any
3\nobreakdash-multi\-sector is a direct sum of line bundles which we use to
compute the orbifold cup product. Finally we compute the
Chen--Ruan cohomology ring of weighted projective space ${\bf
P}^{5}_{1,2,2,3,3,3}$.
Keywords:Chen--Ruan cohomology, twisted sectors, toric varieties, weighted projective space, localization Categories:14N35, 53D45 |
2. CJM 2004 (vol 56 pp. 1094)
Cycle-Level Intersection Theory for Toric Varieties This paper addresses the problem of constructing a
cycle-level intersection theory for toric varieties.
We show that by making one global choice,
we can determine a cycle representative
for the intersection of an equivariant Cartier divisor with an invariant
cycle on a toric variety. For a toric variety
defined by a fan in $N$, the choice consists of giving an
inner product or a complete flag for $M_\Q=
\Qt \Hom(N,\mathbb{Z})$, or more
generally giving for each cone $\s$ in the fan a linear subspace of
$M_\Q$ complementary to $\s^\perp$, satisfying certain compatibility
conditions.
We show that these intersection cycles have properties analogous to the
usual intersections modulo rational equivalence.
If $X$ is simplicial (for instance, if $X$ is non-singular),
we obtain a commutative ring structure
to the invariant cycles of $X$ with rational
coefficients. This ring structure determines cycles representing
certain characteristic classes of the toric variety.
We also discuss
how to define intersection cycles that require no choices,
at the expense of increasing
the size of the coefficient field.
Keywords:toric varieties, intersection theory Categories:14M25, 14C17 |