Abstract
The set of translation planes with spreads in $PG(3,q)$ admitting cyclic affine homology groups of order $q+1$ is shown to be equivalent to the set of flocks of quadratic cones in $PG(3,q)$. The analysis is general and considers analogous homology groups in $PG(3,K)$, for $K$ an arbitrary field and corresponding partial flocks of quadratic cones in $PG(3,K)$.
Citation
N.L. Johnson. "Homology groups of translation planes and flocks of quadratic cones, I. The structure." Bull. Belg. Math. Soc. Simon Stevin 12 (5) 827 - 844, January 2006. https://doi.org/10.36045/bbms/1136902619
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