On partial ovoids of Hermitian surfaces | Zendy

Angela Aguglia | Zendy; G. L. Ebert | Zendy; Deirdre Luyckx | Zendy

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On partial ovoids of Hermitian surfaces

Author(s) -

Angela Aguglia,

G. L. Ebert,

Deirdre Luyckx

Publication year - 2006

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1136902602

Subject(s) - ovoid , hermitian matrix , mathematics , conjecture , degenerate energy levels , pure mathematics , combinatorics , physics , geometry , quantum mechanics

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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