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Characterizations of quadric and Hermitian Veroneseans over finite fields

Characterizations of quadric and Hermitian Veroneseans over finite fields In Hirschfeld and Thas [5] the most important characterizations of quadric Veroneseans are surveyed. However a few difficult cases were still open, in particular the even case. In [10, 11] Thas and Van Maldeghem not only solve all open cases, but they also generalize most of these characterizations in several ways: they do not restrict themselves to the quadric Veronesean of the plane PG $(2,q) $ , they allow ovals instead of conics, and they also characterize projections of quadric Veroneseans. Further, Cooperstein, Thas and Van Maldeghem [1] contains some properties of Hermitian Veroneseans over finite fields and also these varieties and some of their projections are characterized. All these results on Veroneseans will be surveyed here. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Geometry Springer Journals

Characterizations of quadric and Hermitian Veroneseans over finite fields

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Birkhäuser Verlag Basel,
Subject
Mathematics; Geometry
ISSN
0047-2468
eISSN
1420-8997
DOI
10.1007/s00022-003-1703-1
Publisher site
See Article on Publisher Site

Abstract

In Hirschfeld and Thas [5] the most important characterizations of quadric Veroneseans are surveyed. However a few difficult cases were still open, in particular the even case. In [10, 11] Thas and Van Maldeghem not only solve all open cases, but they also generalize most of these characterizations in several ways: they do not restrict themselves to the quadric Veronesean of the plane PG $(2,q) $ , they allow ovals instead of conics, and they also characterize projections of quadric Veroneseans. Further, Cooperstein, Thas and Van Maldeghem [1] contains some properties of Hermitian Veroneseans over finite fields and also these varieties and some of their projections are characterized. All these results on Veroneseans will be surveyed here.

Journal

Journal of Geometry – Springer Journals

Published: Jun 1, 2003

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