We show that a non-degenerate Hermitian variety H(2n, q<sup>2</sup>) in PG(2n, q<sup>2</sup>) can be partitioned in Baer parabolic quadrics Q(2n, q), if q is odd, or in Baer symplectic spaces W(2n−1, q), if q is even.We construct a partial spread of H(4, q<sup>2</sup>) of size (q<sup>5</sup>+1)/(q+1), admitting a group of order (q<sup>5</sup>+1)/(q+1) and a hyperoval of size 2(q<sup>5</sup>+1)/(q+1) on DH(4, q<sup>2</sup>), the point line dual generalized quadrangle of H(4, q<sup>2</sup>), admitting a dihedral group of order 2(q<sup>5</sup> + 1)/(q + 1).

On Singer action on Hermitian varieties / Pavese, Francesco. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - 106:1(2015), pp. 19-27. [10.1007/s00022-014-0227-1]

On Singer action on Hermitian varieties

PAVESE, Francesco
2015-01-01

Abstract

We show that a non-degenerate Hermitian variety H(2n, q2) in PG(2n, q2) can be partitioned in Baer parabolic quadrics Q(2n, q), if q is odd, or in Baer symplectic spaces W(2n−1, q), if q is even.We construct a partial spread of H(4, q2) of size (q5+1)/(q+1), admitting a group of order (q5+1)/(q+1) and a hyperoval of size 2(q5+1)/(q+1) on DH(4, q2), the point line dual generalized quadrangle of H(4, q2), admitting a dihedral group of order 2(q5 + 1)/(q + 1).
2015
On Singer action on Hermitian varieties / Pavese, Francesco. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - 106:1(2015), pp. 19-27. [10.1007/s00022-014-0227-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/81328
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