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On the Betti numbers of the real part of a three-dimensional torus embedding

100%

Ratajski J.

Colloquium Mathematicum

1993

tom 64

nr 1

59-64

Let X be the three-dimensional, complete, nonsingular, complex torus embedding corresponding to a fan $S ⊆ ℝ^{3}$ and let V be the real part of X (for definitions see [1] or [3]). The aim of this note is to give a simple combinatorial formula for calculating the Betti numbers of V.

A Pieri-type formula for even orthogonal Grassmannians

63%

Pragacz P., Ratajski J.

Fundamenta Mathematicae

2003

tom 178

nr 1

49-96

We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred permutations" with even numbers of bars, and divided differences associated with the even orthogonal group SO(2m).

Ograniczanie wyników

1 Colloquium Mathematicum

1 Fundamenta Mathematicae

2 Ratajski J.

1 Pragacz P.

1 2003

1 1993

Wyniki wyszukiwania

On the Betti numbers of the real part of a three-dimensional torus embedding

A Pieri-type formula for even orthogonal Grassmannians