Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
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Ulrich Dempwolff
Abstract
By [4] a doubly transitive, non-solvable dimensional dual hyperoval D is isomorphic either to the Mathieu dual hyperoval or to a quotient of a Huybrechts dual hyperoval. In order to determine all doubly transitive dimensional dual hyperovals, it remains to classify the solvable ones, and this paper is a contribution to this problem. A doubly transitive, solvable dimensional dual hyperoval D of rank n is defined over 𝔽2 and has an automorphism of the form ES, where E is elementary abelian of order 2n and S ≤ Γ L(1, 2n); see Yoshiara [12]. The known examples D are bilinear. In [1] the bilinear, doubly transitive, solvable dimensional dual hyperovals D of rank n with GL(1, 2n) ≤ S are classified. Here we present two new classes of non-bilinear, doubly transitive dimensional dual hyperovals. We also consider universal covers of doubly transitive dimensional dual hyperovals, since they are again doubly transitive dimensional dual hyperovals by [2, Cor. 1.3]. We determine the universal covers of the presently known doubly transitive dimensional dual hyperovals.
Communicated by: W. M. Kantor
Acknowledgements
We thank the referee for helpful comments that lead to a significantly more transparent text.
References
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Articles in the same Issue
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- On mixed Lp John ellipsoids
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- The Bonnet problem for harmonic maps to the three-sphere
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- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
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Articles in the same Issue
- Frontmatter
- A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions
- On mixed Lp John ellipsoids
- Valuations on convex functions and convex sets and Monge–Ampère operators
- Weierstrass points on Kummer extensions
- The Bonnet problem for harmonic maps to the three-sphere
- Maximal arcs in projective planes of order 16 and related designs
- On the decomposition of the small diagonal of a K3 surface
- Doubly transitive dimensional dual hyperovals: universal covers and non-bilinear examples
- Higgs bundles and fundamental group schemes
- A relation between the curvature ellipse and the curvature parabola
- Non-orientable three-submanifolds of G2-manifolds
- The growth of the first non-Euclidean filling volume function of the quaternionic Heisenberg group
- A class of analytic pairs of conjugate functions in dimension three
