Hodge type of projective varieties of low degree
The paper is devoted to the proof of the following result [conjectured by \textit{P. Deligne} and \textit{A. Dimca} in Ann. Sci. Éc. Norm. Supér., IV. Sér. 23, No. 4, 645-656 (1990; Zbl 0743.14028)]: Let \(S\) be a complex projective variety defined in the \(n\)-dimensional projective space by equations of degrees \(d_ 1\geq\cdots\geq d_ r\). Then the Hodge type of \(S\) is at least the integral part of \[ (n-d_ 2-\cdots-d_ r)/d_ 1. \] Two proofs of this fact are given: one based on Nori's deformation theoretic technique and another inspired from \textit{T. Terasoma}'s use of the ``universal pencil'' [cf. Ann. Math., II. Ser. 132, 213-235 (1990; Zbl 0732.14005)].
scientific article; zbMATH DE number 126336