{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833428,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\Delta$ be a symplectic dual polar space $DW(2n-1,{\\Bbb K})$ or a Hermitian dual polar space $DH(2n-1,{\\Bbb K},\\theta)$, $n \\geq 2$. We define a class of hyperplanes of $\\Delta$ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space $DH(2n-1,{\\Bbb K},\\theta)$ arising from its Grassmann-embedding if and only if there exists an empty $\\theta$-Hermitian variety in ${\\rm PG}(n-1,{\\Bbb K})$. Using this result we are able to give the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding. These are also the first examples of ovoids in thick dual polar spaces of rank at least 3 for which the construction does not make use of transfinite recursion.<\/jats:p>","DOI":"10.37236\/90","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:37:00Z","timestamp":1578717420000},"source":"Crossref","is-referenced-by-count":4,"title":["On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces"],"prefix":"10.37236","volume":"16","author":[{"given":"Bart","family":"De Bruyn","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r1\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:14:51Z","timestamp":1579317291000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/90","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,1,7]]},"article-number":"R1"}}