Real flats tangent to quadrics in
Authors:
Frank Sottile and Thorsten Theobald
Journal:
Proc. Amer. Math. Soc. 133 (2005), 28352844
MSC (2000):
Primary 14N10, 51M30, 14P99, 52C45, 05A19
Published electronically:
April 8, 2005
MathSciNet review:
2159760
Fulltext PDF Free Access
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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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Common tangents to four unit balls in . Discrete Comput. Geom. 26:117, 2001. MR 1832726 (2002f:51023)
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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 62, Technische Universität Berlin, Strasse des 17. Juni 1936, D10623 Berlin, Germany
Email:
theobald@math.tuberlin.de
DOI:
http://dx.doi.org/10.1090/S0002993905078809
PII:
S 00029939(05)078809
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 DMS0070494 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.
