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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 10, Issue 1


Secant dimensions of low-dimensional homogeneous varieties

Karin Baur / Jan Draisma
  • Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, and Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands. Email:
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Published Online: 2010-02-01 | DOI: https://doi.org/10.1515/advgeom.2010.001


We completely describe the higher secant dimensions of all connected homogeneous projective varieties of dimension at most 3, in all possible equivariant embeddings. In particular, we calculate these dimensions for all Segre–Veronese embeddings of ℙ1 × ℙ1, ℙ1 × ℙ1 × ℙ1, and ℙ2 × ℙ1, as well as for the flag variety ℱ of incident point-line pairs in ℙ2. For ℙ2 × ℙ1 and ℱ the results are new, while the proofs for the other two varieties are more compact than existing proofs. Our main tool is the second author's tropical approach to secant dimensions.

About the article

Received: 2007-07-19

Revised: 2009-02-09

Published Online: 2010-02-01

Published in Print: 2010-01-01

Citation Information: Advances in Geometry, Volume 10, Issue 1, Pages 1–29, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.001.

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