TY - JOUR
T1 - On m-ovoids of Q+(7, q) with q odd
AU - Adriaensen, Sam
AU - Mannaert, Jonathan
AU - De Beule, Jan
AU - Grimaldi, Giovanni
N1 - Funding Information:
The research of Giovanni Giuseppe Grimaldi was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM, contract number CUP E55F22000270001 ). The authors also want to thank the referees for their valuable suggestions to improve this article.
Publisher Copyright:
© 2024 Elsevier Inc.
PY - 2024/3
Y1 - 2024/3
N2 - In this paper, we provide a construction of (q+1)-ovoids of the hyperbolic quadric Q+(7,q), q an odd prime power, by glueing (q+1)/2-ovoids of the elliptic quadric Q−(5,q). This is possible by controlling some intersection properties of (putative) m-ovoids of elliptic quadrics. It eventually yields (q+1)-ovoids of Q+(7,q) not coming from a 1-system. Secondly, for certain values of q, we construct line spreads of PG(3,q) that have as many secants to a given elliptic quadric as possible. This is then used to construct m-ovoids for m∈{2,4,6,8,10} in Q+(7,3).
AB - In this paper, we provide a construction of (q+1)-ovoids of the hyperbolic quadric Q+(7,q), q an odd prime power, by glueing (q+1)/2-ovoids of the elliptic quadric Q−(5,q). This is possible by controlling some intersection properties of (putative) m-ovoids of elliptic quadrics. It eventually yields (q+1)-ovoids of Q+(7,q) not coming from a 1-system. Secondly, for certain values of q, we construct line spreads of PG(3,q) that have as many secants to a given elliptic quadric as possible. This is then used to construct m-ovoids for m∈{2,4,6,8,10} in Q+(7,3).
UR - http://www.scopus.com/inward/record.url?scp=85185536033&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2024.102387
DO - 10.1016/j.ffa.2024.102387
M3 - Article
VL - 95
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
SN - 1071-5797
M1 - 102387
ER -