N\'eron-Severi group of a general hypersurface

TL;DR

This paper generalizes a classical theorem about the Picard group of surfaces to the Néron-Severi group of hypersurfaces in smooth projective varieties, broadening understanding of algebraic cycles in higher dimensions.

Contribution

It extends Lopez's theorem from surfaces to hypersurfaces in arbitrary smooth projective varieties, focusing on the intermediate Néron-Severi group.

Findings

Generalization of Lopez's theorem to higher dimensions

Description of the Néron-Severi group for general hypersurfaces

Broader understanding of algebraic cycles in algebraic geometry

Abstract

In this paper we extend the well known theorem of Angelo Lopez concerning the Picard group of the general space projective surface containing a given smooth projective curve, to the intermediate N\'eron-Severi group of a general hypersurface in any smooth projective variety.