A numerical transcendental method in algebraic geometry: Computation of Picard groups and related invariants - INRIA - Institut National de Recherche en Informatique et en Automatique Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Applied Algebra and Geometry Année : 2019

A numerical transcendental method in algebraic geometry: Computation of Picard groups and related invariants

Résumé

Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces in P3. As an application, we count the number of rational curves of a given degree lying on each surface. For quartic surfaces we also compute the endomorphism ring of their transcendental lattice. The method applies more generally to the computation of the lattice generated by Hodge cycles of middle dimension on smooth projective hypersurfaces. We demonstratethe method by a systematic study of thousands of quartic surfaces (K3 surfaces) defined by sparse polynomials. The results are only supported by strong numerical evidence; yet, the possibility of error is quantified in intrinsic terms, like the degree of curves generating the Picard group.
Fichier principal
Vignette du fichier
numtranscmeth (1).pdf (430.39 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01932147 , version 1 (23-11-2018)
hal-01932147 , version 2 (21-10-2020)

Identifiants

Citer

Pierre Lairez, Emre Can Sertöz. A numerical transcendental method in algebraic geometry: Computation of Picard groups and related invariants. SIAM Journal on Applied Algebra and Geometry, 2019, 3 (4), pp.559-584. ⟨10.1137/18M122861X⟩. ⟨hal-01932147v2⟩
173 Consultations
435 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More