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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Real rational curves in Grassmannians
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by Frank Sottile PDF
J. Amer. Math. Soc. 13 (2000), 333-341 Request permission

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
  • MR Author ID: 355336
  • ORCID: 0000-0003-0087-7120
  • Email: sottile@math.umass.edu
  • 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.
  • © Copyright 2000 American Mathematical Society
  • 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
  • MathSciNet review: 1706484