2
$\begingroup$

I am looking for a reference from which I can cite the following statement:

The Picard group of a very general quartic hypersurface $X\subset\mathbb{P}^3$ is generated by the class of a hyperplane section.

What is the standard reference for this?

Improve this question
$\endgroup$
1
  • 6
    $\begingroup$ This is called the Noether-Lefschetz theorem. Modern proofs can be found in many places, e.g. in Voisin, Hodge theory and Complex AG II $\endgroup$
    – Donu Arapura
    Commented Dec 2, 2020 at 17:10

1 Answer 1

Reset to default
6
$\begingroup$

That is the Noether-Lefschetz theorem. Searching online should find plenty of results in web pages and lecture notes. If you want a published source, how about: Mark Green, A new proof of the explicit Noether-Lefschetz theorem, J. Differential Geom. 27 (1988), no. 1, 155–159.

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .