Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space

Details Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space Explicit Enumerative Geometry for the Real Grassmannian of Lines in Projective Space

1995-10-31

arxiv.org/abs/alg-geom/9510017v1

Duke Math. J., 87 (1997) 59-85

Mathematics

Algebraic Geometry

LaTeX 2e, 18 pages with three figures

Scientific paper

We extend the classical Schubert calculus of enumerative geometry for the Grassmann variety of lines in projective space from the complex realm to the real. Specifically, given any collection of Schubert conditions on lines in projective space which generically determine a finite number of lines, we show there exist real generic conditions determining the expected number of real lines. Our main tool is an explicit description of rational equivalences which also constitutes a novel determination of the Chow rings of these Grassmann varieties.

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