Abstract. Let X ⊂ PN 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 P6 with one 4-secant plane through the general point of P6.
A SEVERI TYPE THEOREM FOR SURFACES IN P6 / de poi, Pietro; Ilardi, Giovanna. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - Volume 149:2(2021), pp. 591-605. [10.1090/proc/15263]
A SEVERI TYPE THEOREM FOR SURFACES IN P6
de poi, pietro;Giovanna Ilardi
2021
Abstract
Abstract. Let X ⊂ PN 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 P6 with one 4-secant plane through the general point of P6.| File | Dimensione | Formato | |
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