On invariant notions of Segre varieties in binary projective spaces View Full Text


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Article Info

DATE

2012-03

AUTHORS

Hans Havlicek, Boris Odehnal, Metod Saniga

ABSTRACT

Invariant notions of a class of Segre varieties of PG(2m − 1, 2) that are direct products of m copies of PG(1, 2), m being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains and is invariant under its projective stabiliser group . By embedding PG(2m − 1, 2) into PG(2m − 1, 4), a basis of the latter space is constructed that is invariant under as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as m is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a -invariant geometric spread of lines of PG(2m − 1, 2). This spread is also related with a -invariant non-singular Hermitian variety. The case m = 3 is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under , while the points of PG(7, 2) form five orbits. More... »

PAGES

343-356

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URI

http://scigraph.springernature.com/pub.10.1007/s10623-011-9525-x

DOI

http://dx.doi.org/10.1007/s10623-011-9525-x

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https://app.dimensions.ai/details/publication/pub.1044317365


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136 schema:name Institut für Diskrete Mathematik und Geometrie, Technische Universität, Wiedner Hauptstraße 8–10/104, 1040, Wien, Austria
137 rdf:type schema:Organization
 




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