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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
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 $p$-planes incident on some given general subspaces, there are general real subspaces such that each of the (finitely many) incident $p$-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: http://dx.doi.org/10.1090/S0894-0347-99-00323-9
PII: S 0894-0347(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