We study eggs in $PG(4n-1,q)$. A new model for eggs is presented in which all known examples are given. We calculate the general form of the dual egg for eggs arising from a semifield flock. Applying this to the egg obtained in L. Bader, G. Lunardon and I. Pinneri \cite{BALUPI} from the Penttila-Williams ovoid \cite{PEWI}, we obtain the dual egg, which is not isomorphic to any of the previous known examples, see \cite{BALUPI}. Furthermore we give a new proof of a conjecture of J.A.Thas \cite{TH1} using our model, and classify all eggs of $PG(7,2)$ which is equivalent to the classification of all translation generalised quadrangles of order (4,16).
On eggs and translation generalised quadrangles
LAVRAUW, MICHEL;
2001
Abstract
We study eggs in $PG(4n-1,q)$. A new model for eggs is presented in which all known examples are given. We calculate the general form of the dual egg for eggs arising from a semifield flock. Applying this to the egg obtained in L. Bader, G. Lunardon and I. Pinneri \cite{BALUPI} from the Penttila-Williams ovoid \cite{PEWI}, we obtain the dual egg, which is not isomorphic to any of the previous known examples, see \cite{BALUPI}. Furthermore we give a new proof of a conjecture of J.A.Thas \cite{TH1} using our model, and classify all eggs of $PG(7,2)$ which is equivalent to the classification of all translation generalised quadrangles of order (4,16).Pubblicazioni consigliate
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