A Severi type theorem for surfaces in ℙ⁶

De Poi, Pietro; Ilardi, Giovanna

doi:10.1090/proc/15263

A Severi type theorem for surfaces in $\mathbb {P}^6$
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by Pietro De Poi and Giovanna Ilardi

Proc. Amer. Math. Soc. 149 (2021), 591-605

DOI: https://doi.org/10.1090/proc/15263

Published electronically: December 16, 2020

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Corrigendum: Proc. Amer. Math. Soc. (to appear).

Abstract:

Let $X \subset \mathbb {P}^N$ be a projective, non-degenerate, irreducible smooth variety of dimension $n$. After giving the definition of generalised OADP-variety (one apparent double point), i.e. varieties $X$ such that:

$n(k+1) - (N-r)(k-r) + r = N$,

there is one apparent $(k+1)$-secant $(r-1)$-space to a generic projection of $X$ from a point,

we concentrate in studying generalised OADP-surfaces in low dimensional projective spaces, and the main result of this paper is the classification of smooth surfaces in $\mathbb {P}^6$ with one $4$-secant plane through the general point of $\mathbb {P}^6$.

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