A triple intersection theorem for the varieties of SO(n)/Pd

Date

1993

Authors

Sertöz, S.

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Abstract

We study the Schubert calculus on the space of d-dimensional linear subspaces of a smooth n-dimensional quadric lying in the projective space. Following Hodge and Pedoe we develop the intersection theory of this space in a purely combinatorial manner. We prove in particular that if a triple intersection of Schubert cells on this space is nonempty then a certain combinatorial relation holds among the Schubert symbols involved, similar to the classical one. We also show when these necessary conditions are also sufficient to obtain a nontrivial intersection. Several examples are calculated to illustrate the main results.

Source Title

Fundamenta Mathematicae

Publisher

Polish Academy of Sciences, Institute of Mathematics

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Published Version (Please cite this version)

Language

English