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Rational functions and real Schubert calculus
Author(s):
A.
Eremenko;
A.
Gabrielov;
M.
Shapiro;
A.
Vainshtein
Journal:
Proc. Amer. Math. Soc.
134
(2006),
949-957.
MSC (2000):
Primary 14P05;
Secondary 26C15
Posted:
July 25, 2005
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Abstract:
We single out some problems of Schubert calculus of subspaces of codimension  that have the property that all their solutions are real whenever the data are real. Our arguments explore the connection between subspaces of codimension  and rational functions of one variable.
References:
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- A. Eremenko and A. Gabrielov, Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry, Ann. Math., 155 (2002), 105-129. MR 1888795 (2003c:58028)
- 2.
- A. Eremenko and A. Gabrielov, Wronski map and Grassmannians of real codimension 2 subspaces, Computational Methods and Function Theory, 1 (2001) 1-25. MR 1931599 (2003h:26022)
- 3.
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- W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, 1948. MR 0006493 (3,312b)
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- L. Manivel, Symmetric functions, Schubert Polynomials and degeneracy loci, AMS, Providence, RI, 2001. MR 1852463 (2002h:05161)
- 6.
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- 8.
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Additional Information:
A.
Eremenko
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Email:
eremenko@math.purdue.edu
A.
Gabrielov
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Email:
agabriel@math.purdue.edu
M.
Shapiro
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
mshapiro@math.msu.edu
A.
Vainshtein
Affiliation:
Department of Computer Science, University of Haifa, Mount Carmel, 31905 Haifa, Israel
Email:
alek@cs.haifa.ac.il
DOI:
10.1090/S0002-9939-05-08048-2
PII:
S 0002-9939(05)08048-2
Received by editor(s):
August 25, 2004
Received by editor(s) in revised form:
October 29, 2004
Posted:
July 25, 2005
Additional Notes:
The authors were supported by NSF grants DMS-0100512 and DMS-0244421 (A.E.), DMS-0200861 and DMS-0245628 (A.G.), and DMS-0401178 (M.S.); and by the BSF grant 2002375 (M.S. and A.V.) and by the Institute of Quantum Science, MSU (M.S.).
Communicated by:
John R. Stembridge
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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