• Corpus ID: 236447562

The Noether--Lefschetz theorem

  title={The Noether--Lefschetz theorem},
  author={Lena Ji},
  • L. Ji
  • Published 28 July 2021
  • Mathematics
We show that if X ⊂ P k is a normal variety of dimension n ≥ 3 and H ⊂ P k a very general hypersurface of degree d = 4 or ≥ 6, then the restriction map Cl(X) → Cl(X ∩H) is an isomorphism up to torsion. If n ≥ 4, the result holds for d ≥ 2. 



Moishezon's theorem and degeneration

The Noether–Lefschetz theorem for the divisor class group

Ample subvarieties of algebraic varieties

Ample divisors.- Affine open subsets.- Generalization to higher codimensions.- The grothendieck-lefschetz theorems.- Formal-rational functions along a subvariety.- Algebraic geometry and analytic

Hodge theory and complex algebraic geometry

Introduction. Part I. The Topology of Algebraic Varieties: 1. The Lefschetz theorem on hyperplane sections 2. Lefschetz pencils 3. Monodromy 4. The Leray spectral sequence Part II. Variations of

The Grothendieck-Lefschetz theorem for normal projective varieties

We prove that for a normal projective variety X in characteristic 0, and a base-point free ample line bundle L on it, the restriction map of divisor class groups Cl(X) → Cl(Y ) is an isomorphism for

Noether-Lefschetz Theorem and applications

In this paper we generalize the classical Noether-Lefschetz Theorem (see [7], [5]) to arbitrary smooth projective threefolds. More specifically, we prove that given any smooth projective threefold X

The Tate conjecture for K3 surfaces over finite fields

Artin’s conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin’s conjecture over fields of characteristic p≥5. This implies Tate’s

Néron–Severi groups under specialization

Andr\'e used Hodge-theoretic methods to show that in a smooth proper family X to B of varieties over an algebraically closed field k of characteristic 0, there exists a closed fiber having the same

Restriction of Sections for Families of Abelian Varieties

Given a family of Abelian varieties over a positive-dimensional base, we prove that for a sufficiently general curve in the base, every rational section of the family over the curve is contained in a


In this paper, the relation between the algebraic homology classes on a protective algebraic variety and on its 'general' hyperplane section is studied. It is proved in particular that on a 'general'