Enumerative geometry for real varieties

Details Enumerative geometry for real varieties Enumerative geometry for real varieties

1996-09-12

arxiv.org/abs/alg-geom/9609007v1

Proc. Sympos. Pure Math., Vol 62.1, 1997 pp. 435-447

Mathematics

Algebraic Geometry

Based upon the Author's talk at 1995 AMS Summer Research Institute in Algebraic geometry. To appear in the Proceedings. 11 pag

Scientific paper

We discuss the problem of whether a given problem in enumerative geometry can have all of its solutions be real. In particular, we describe an approach to problems of this type, and show how this can be used to show some enumerative problems involving the Schubert calculus on Grassmannians may have all of their solutions be real. We conclude by describing the work of Fulton and Ronga-Tognoli-Vust, who (independently) showed that there are 5 real plane conics such that each of the 3264 conics tangent to all five are real.

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