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

Fundamenta Mathematicae (1993)

- Volume: 142, Issue: 3, page 201-220
- ISSN: 0016-2736

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topSertöz, S.. "A triple intersection theorem for the varieties SO(n)/Pd." Fundamenta Mathematicae 142.3 (1993): 201-220. <http://eudml.org/doc/211982>.

@article{Sertöz1993,

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.},

author = {Sertöz, S.},

journal = {Fundamenta Mathematicae},

keywords = {subspaces of a quadric; Schubert calculus; intersection theory; intersection of Schubert cells},

language = {eng},

number = {3},

pages = {201-220},

title = {A triple intersection theorem for the varieties SO(n)/Pd},

url = {http://eudml.org/doc/211982},

volume = {142},

year = {1993},

}

TY - JOUR

AU - Sertöz, S.

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

JO - Fundamenta Mathematicae

PY - 1993

VL - 142

IS - 3

SP - 201

EP - 220

AB - 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.

LA - eng

KW - subspaces of a quadric; Schubert calculus; intersection theory; intersection of Schubert cells

UR - http://eudml.org/doc/211982

ER -

## References

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- [7] W. V. D. Hodge and D. Pedoe, Methods of Algebraic Geometry, Vol. II, Cambridge University Press, 1968. Zbl0157.27501
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- [10] P. Pragacz, Geometric applications of symmetric polynomials, preprint, Max-Planck Institut für Mathematik, Bonn 1992.
- [11] P. Pragacz and J. Ratajski, Pieri for isotropic Grassmannians: the operator approach, preprint, Max-Planck Institut für Mathematik, Bonn 1992.