{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:52Z","timestamp":1753893832302,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $V$ be a\u00a0 $(d+1)$-dimensional vector space over a field $\\mathbb{F}$. Sesquilinear forms over $V$ have been largely studied when they are reflexive and hence give rise to a (possibly degenerate) polarity of\u00a0 the $d$-dimensional projective space $\\mathrm{PG}(V)$.\u00a0 Everything is known in this case for both degenerate and non-degenerate reflexive forms if\u00a0 $\\mathbb{F}$\u00a0 is either\u00a0 ${\\mathbb R}$, ${\\mathbb C}$ or a finite field\u00a0 ${\\mathbb F}_q$. \u00a0 In this paper we consider\u00a0 degenerate, non-reflexive sesquilinear forms of $V=\\mathbb{F}_{q^n}^3$. We will see that these forms give rise to degenerate correlations of $\\mathrm{PG}(2,q^n)$ whose set of absolute points are, besides cones,\u00a0 the (possibly degenerate) $C_F^m$-sets studied by Donati and Durante in 2014. In the final section we collect some\u00a0 results from the huge work of B.C. Kestenband\u00a0 regarding what is known for the set of\u00a0 the absolute\u00a0 points\u00a0 of correlations in $\\mathrm{PG}(2,q^n)$ induced\u00a0 by a\u00a0 non-degenerate, non-reflexive sesquilinear form of $V=\\mathbb{F}_{q^n}^3$.<\/jats:p>","DOI":"10.37236\/8920","type":"journal-article","created":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:19:54Z","timestamp":1590718794000},"source":"Crossref","is-referenced-by-count":2,"title":["On Absolute Points of Correlations of $\\mathrm{PG}(2,q^n)$"],"prefix":"10.37236","volume":"27","author":[{"given":"Jozefien","family":"D'haeseleer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola","family":"Durante","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,5,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p32\/8088","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i2p32\/8088","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T02:19:55Z","timestamp":1590718795000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i2p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,29]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,4,3]]}},"URL":"https:\/\/doi.org\/10.37236\/8920","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,5,29]]},"article-number":"P2.32"}}