A family of m-ovoids of parabolic quadrics

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• 作者：Tao Feng^a ; ¹ ; ^{tfeng@zju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Koji Momihara^b ; ² ; ^{momihara@educ.kumamoto-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Qing Xiang^c ; ^{xiang@math.udel.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized quadrangle ; m-ovoid ; Ovoid ; Polar space ; Quadric ; Tight set
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：140
• 期：Complete
• 页码：97-111
• 全文大小：387 K

文摘

We construct a family of $\frac{(q-1)}{2}$-ovoids of Q(4,q)$Q(4,q)$, the parabolic quadric of PG(4,q)$\mathrm{PG}(4,q)$, for $q\equiv 3(\mathrm{mod}4)$. The existence of $\frac{(q-1)}{2}$-ovoids of Q(4,q)$Q(4,q)$ was only known for q=3,7$q=3,7$, or 11. Our construction provides the first infinite family of $\frac{(q-1)}{2}$-ovoids of Q(4,q)$Q(4,q)$. Along the way, we also give a construction of $\frac{(q+1)}{2}$-ovoids in Q(4,q)$Q(4,q)$ for $q\equiv 1(\mathrm{mod}4)$.