Real -flats tangent to quadrics in

Authors:
Frank Sottile and Thorsten Theobald

Journal:
Proc. Amer. Math. Soc. **133** (2005), 2835-2844

MSC (2000):
Primary 14N10, 51M30, 14P99, 52C45, 05A19

DOI:
https://doi.org/10.1090/S0002-9939-05-07880-9

Published electronically:
April 8, 2005

MathSciNet review:
2159760

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and denote the dimension and the degree of the Grassmannian , respectively. For each there are (a priori complex) -planes in tangent to general quadratic hypersurfaces in . We show that this class of enumerative problems is fully real, i.e., for there exists a configuration of real quadrics in (affine) real space so that all the mutually tangent -flats are real.

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Additional Information

**Frank Sottile**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843

Email:
sottile@math.tamu.edu

**Thorsten Theobald**

Affiliation:
Institut für Mathematik, MA 6-2, Technische Universität Berlin, Strasse des 17. Juni 1936, D-10623 Berlin, Germany

Email:
theobald@math.tu-berlin.de

DOI:
https://doi.org/10.1090/S0002-9939-05-07880-9

Keywords:
Tangents,
transversals,
quadrics,
enumerative geometry,
real solutions,
Grassmannian

Received by editor(s):
March 11, 2004

Received by editor(s) in revised form:
May 25, 2004

Published electronically:
April 8, 2005

Additional Notes:
The research of the first author was supported by NSF CAREER grant DMS-0070494 and the Clay Mathematical Institute

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.