Real rational curves in Grassmannians

Author:
Frank Sottile

Journal:
J. Amer. Math. Soc. **13** (2000), 333-341

MSC (2000):
Primary 14M15, 14N35, 14P99, 65H20, 93B55

DOI:
https://doi.org/10.1090/S0894-0347-99-00323-9

Published electronically:
October 25, 1999

MathSciNet review:
1706484

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Abstract: Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with respect to some given general figures. For the problem of plane conics tangent to five general (real) conics, the surprising answer is that all 3264 may be real. Similarly, given any problem of enumerating -planes incident on some given general subspaces, there are general real subspaces such that each of the (finitely many) incident -planes is real. We show that the problem of enumerating parameterized rational curves in a Grassmannian satisfying simple (codimension 1) conditions may have all of its solutions real.

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Additional Information

**Frank Sottile**

Affiliation:
Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388

Address at time of publication:
Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003-4515

Email:
sottile@math.umass.edu

DOI:
https://doi.org/10.1090/S0894-0347-99-00323-9

Received by editor(s):
April 29, 1999

Received by editor(s) in revised form:
August 24, 1999

Published electronically:
October 25, 1999

Additional Notes:
Research at MSRI supported in part by NSF grant DMS-9701755.

Article copyright:
© Copyright 2000
American Mathematical Society