On the duals of smooth projective complex hypersurfaces

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Alexandru Dimca
Université Côte d'Azur
https://orcid.org/0000-0001-9679-9870
Giovanna Ilardi
Università degli Studi di Napoli Federico II. Dipartimento Matematica Ed Applicazioni "R. Caccioppoli"
https://orcid.org/0000-0001-9578-4992

We first show that a generic hypersurface V of degree d ≥ 3 in the projective complex space P n of dimension n ≥ 3 has at least one hyperplane section V ∩H containing exactly n ordinary double points, alias A1 singularities, in general position, and no other singularities. Equivalently, the dual hypersurface V ∨ has at least one normal crossing singularity of multiplicity n. Using this result, we show that the dual of any smooth hypersurface with n, d ≥ 3 has at least a very singular point q, in particular a point q of multiplicity ≥ n.

Paraules clau
Hypersurface, Dual hypersurface, Lefschetz properties, Hyperplane section, Singularities

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Dimca, Alexandru; Ilardi, Giovanna. «On the duals of smooth projective complex hypersurfaces». Publicacions Matemàtiques, 2024, vol.VOL 68, núm. 2, p. 431-8, http://raco.cat/index.php/PublicacionsMatematiques/article/view/430118.
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