The special Schubert calculus is real
Author:
Frank Sottile
Journal:
Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 35-39
MSC (1991):
Primary 14P99, 14N10, 14M15, 14Q20; Secondary 93B55
DOI:
https://doi.org/10.1090/S1079-6762-99-00058-X
Published electronically:
April 1, 1999
MathSciNet review:
1679451
Full-text PDF Free Access
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Abstract: We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real.
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- B. Huber, F. Sottile, and B. Sturmfels, Numerical Schubert calculus. J. Symb. Comp., 26 (1998), pp. 767–788.
- F. Ronga, A. Tognoli, and T. Vust, The number of conics tangent to 5 given conics: the real case, Rev. Mat. Univ. Complut. Madrid, 10 (1997), pp. 391–421.
- J. Rosenthal and F. Sottile, Some remarks on real and complex output feedback, Systems & Control Lett., 33 (1998), pp. 73–80. . For a description of the computational aspects, see http://www.nd.edu/~rosen/pole/.
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- F. Sottile, Enumerative geometry for the real Grassmannian of lines in projective space, Duke Math. J., 87 (1997), pp. 59–85.
- F. Sottile, Real enumerative geometry and effective algebraic equivalence, J. Pure Appl. Alg., 117 & 118 (1997), pp. 601–615. Proc., MEGA’96.
- F. Sottile, Real Schubert calculus: Polynomial systems and a conjecture of Shapiro and Shapiro. MSRI preprint # 1998-066. For an archive of computations and computer algebra scripts, see http://www.math.wisc.edu/~sottile/pages/shapiro/index.html, 1998.
- J. Verschelde, Numerical evidence of a conjecture in real algebraic geometry. MSRI preprint # 1998-064, 1998.
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Additional Information
Frank Sottile
Affiliation:
Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA 94720
Address at time of publication:
Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706-1388
MR Author ID:
355336
ORCID:
0000-0003-0087-7120
Keywords:
Schubert calculus,
enumerative geometry,
Grassmannian,
pole placement problem
Received by editor(s):
December 20, 1998
Published electronically:
April 1, 1999
Additional Notes:
MSRI preprint # 1998-067.
Research supported by NSF grant DMS-9701755.
Communicated by:
Robert Lazarsfeld
Article copyright:
© Copyright 1999
American Mathematical Society
