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

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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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*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.
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*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