Equivariant structure constants for ordinary and weighted projective space

Abstract

We compute the integral torus-equivariant cohomology ring for weighted projective space for two different torus actions by embedding the cohomology in a sum of polynomial rings ${\oplus }_{i=0}^n\mathbb{Z}[t_1,t_2,...,t_n]$. One torus action gives a result complementing that of Bahri, Franz, and Ray. For the other torus action, each basis class for weighted projective space is a multiple of the basis class for ordinary projective space; we identify each multiple explicitly. We also give a simple formula for the structure constants of the equivariant cohomology ring of ordinary projective space in terms of the basis of Schubert classes, as a sequence of divided difference operators applied to a specific polynomial.

14 pages

References in corpus (1)

• Equivariant Littlewood-Richardson Skew Tableaux