An effective version of Nori's theorem
Recently, \textit{M. V. Nori} [Invent. Math. 111, No. 2, 349-373 (1993)] has shown that a homologically non-trivial cycle on a projective variety \(X\) is algebraically nontrivial on \(Y=X \cap D_ 1\cap \cdots \cap D_ h\), where the \(D_ i\) are divisors on \(X\) of large enough degree. We give a sufficient condition on the positivity of the divisors \(D_ i\), for Nori's theorem to be applicable. - The main ingredient is an effective vanishing theorem for some Koszul type cohomology groups. We also prove an extension of our vanishing theorem which addresses a conjecture of Nori.
scientific article; zbMATH DE number 561282