Work

Non-Density of the Exceptional Components of the Noether–Lefschetz Locus

Year: 2024

Type: article

Abstract: We study when the Picard group of smooth surfaces of degree d ≥ 5 in P3 acquires extra classes. In particular we show that the so-called exceptional components of the Noether–Lefschetz locus are not Zariski dense. This answers a 1991 question of C. Voisin. We also obtain similar results for the Noether–Lefschetz locus for suitable (Y, L), where Y is a smooth projective three-fold and L a very ample line bundle. Both results are applications of the Zilber–Pink viewpoint recently developed by the authors for arbitrary (polarized, integral) variations of Hodge structures.

Source: edoc Publication server (Humboldt University of Berlin)

DOI: 10.18452/34215

Authors: Baldi, Gregorio, Klingler, Bruno, Ullmo, Emmanuel

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6887996965

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