Homology groups of translation planes and flocks of quadratic cones, II; j-planes


The set of j-planes with spreads in PG(3,K), for K a field admitting a quadratic field extension K+ is shown to be equivalent to the set of all det K+-monomial partial flocks of a quadratic cone. Using this connection, when K is GF(2r), the set of j-planes is determined and j = 0, 1, or 2 and correspond to the linear, Walker/Betten or Payne conical flocks, respectively. When K is the field of real numbers, the set of j-planes is completely determined and j is any real number > -½

DOI Code: 10.1285/i15900932v28n1p77

Keywords: hyper-regulus; multiple replacement; André hyper-reguli

Classification: 51E23; 51A40

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