On partial ovoids of Hermitian surfaces


Lower bounds for the size of a complete partial ovoid in a nondegenerate Hermitian surface are obtained. For even characteristic, a sharp bound is obtained and all examples of this size are described. Next, a general construction method for locally hermitian partial ovoids is explained, which leads to interesting small examples. Finally, a conjecture is given for the size of the largest complete strictly partial ovoid. By using partial derivation, several examples of complete strictly partial ovoids of this size are provided.

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@inproceedings{Aguglia2004OnPO, title={On partial ovoids of Hermitian surfaces}, author={Angela Aguglia and Gary L. Ebert and Deirdre Luyckx}, year={2004} }