Unlike the real case, for each q power of a prime it is possible to injectively project the quadric Veronesean of PG(5, q) into a solid or even a plane. Here a finite analogue of the Roman surface of J. Steiner is described. Such analogue arises from an embedding \sigma of PG(2, q) into PG(3, q) mapping any line onto a non-singular conic. Its image PG(2, q)\sigma has a nucleus, say T\sigma, arising from three points of PG(2, q^3 ) forming an orbit of the Frobenius collineation.
On finite Steiner surfaces
ZANELLA, CORRADO
2012
Abstract
Unlike the real case, for each q power of a prime it is possible to injectively project the quadric Veronesean of PG(5, q) into a solid or even a plane. Here a finite analogue of the Roman surface of J. Steiner is described. Such analogue arises from an embedding \sigma of PG(2, q) into PG(3, q) mapping any line onto a non-singular conic. Its image PG(2, q)\sigma has a nucleus, say T\sigma, arising from three points of PG(2, q^3 ) forming an orbit of the Frobenius collineation.
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