# 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

top- [1] E. Artin, Geometric Algebra, Interscience, New York 1988 (c1957).
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- [3] İ. Dibağ, Topology of the complex varieties ${A}_{s}^{\left(n\right)}$, J. Differential Geom. 11 (1976), 499-520.
- [4] W. Fulton, Intersection Theory, Springer, 1984.
- [5] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New York 1978. Zbl0408.14001
- [6] H. Hiller and B. Boe, Pieri formulas for $S{O}_{2}n+1/{U}_{n}$ and $S{p}_{n}/{U}_{n}$, Adv. in Math. 62 (1986), 49-67.
- [7] W. V. D. Hodge and D. Pedoe, Methods of Algebraic Geometry, Vol. II, Cambridge University Press, 1968. Zbl0157.27501
- [8] S. Kleiman and D. Laksov, Schubert calculus, Amer. Math. Monthly 79 (1972), 1061-1082.
- [9] P. Pragacz, Algebro-geometric applications of Schur S- and Q-polynomials, in: Topics in Invariant Theory, Séminaire d'Algèbre Dubreil-Malliavin 1989-1990, Lecture Notes in Math. 1478, Springer, 1991, 130-191.
- [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.

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