{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:10:08Z","timestamp":1760029808184,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let X\u2282Pn, where 3\u2264n\u22645, be an irreducible hypersurface of degree d\u22652. Fix an integer t\u22653. If n=5, assume t\u22654 and (t,d)\u2260(4,2). Using the Differential Horace Lemma, we prove that OX(t) is not secant defective. For a fixed X, our proof uses induction on the integer t. The key points of our method are that for a fixed X, we only need the case of general linear hyperplane sections of X in lower-dimension projective spaces and that we do not use induction on d, allowing an interested reader to tackle a specific X for n&gt;5. We discuss (as open questions) possible extensions of some weaker forms of the theorem to the case where n&gt;5.<\/jats:p>","DOI":"10.3390\/sym17030454","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T11:02:31Z","timestamp":1742295751000},"page":"454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Secant Non-Defectivity of Integral Hypersurfaces of Projective Spaces of at Most Five Dimensions"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1432-7413","authenticated-orcid":false,"given":"Edoardo","family":"Ballico","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Trento, 38123 Trento, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bernardi, A., Carlini, E., Catalisano, M.V., Gimigliano, A., and Oneto, A. 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