A note on relative hemisystems of Hermitian generalised quadrangles
In this paper we introduce a set of sufficient criteria for the construction of relative
hemisystems of the Hermitian space H (3, q^ 2) H (3, q 2), unifying all known infinite families.
We use these conditions to provide new proofs of the existence of the known infinite families
of relative hemisystems. Reproving these results has allowed us to find new relative
hemisystems closely related to an infinite family of Cossidente's, and develop techniques
that are likely to be useful in finding relative hemisystems in future.
hemisystems of the Hermitian space H (3, q^ 2) H (3, q 2), unifying all known infinite families.
We use these conditions to provide new proofs of the existence of the known infinite families
of relative hemisystems. Reproving these results has allowed us to find new relative
hemisystems closely related to an infinite family of Cossidente's, and develop techniques
that are likely to be useful in finding relative hemisystems in future.
Abstract
In this paper we introduce a set of sufficient criteria for the construction of relative hemisystems of the Hermitian space , unifying all known infinite families. We use these conditions to provide new proofs of the existence of the known infinite families of relative hemisystems. Reproving these results has allowed us to find new relative hemisystems closely related to an infinite family of Cossidente’s, and develop techniques that are likely to be useful in finding relative hemisystems in future.
Springer
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