A numerical transcendental method in algebraic geometry

Abstract : Based on high precision computation of periods and lattice reduction techniques, we compute the Picard group of smooth surfaces. We also study the lattice reduction technique that is employed in order to quantify the possibility of numerical error in terms of an intrinsic measure of complexity of each surface. The method applies more generally to the computation of the lattice generated by Hodge cycles of middle dimension on smooth projective hypersurfaces. We demonstrate the method by a systematic study of thousands of quartic surfaces (K3s) defined by sparse polynomials. 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.
Type de document :
Pré-publication, Document de travail
2018
Liste complète des métadonnées

Littérature citée [8 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01932147
Contributeur : Pierre Lairez <>
Soumis le : vendredi 23 novembre 2018 - 08:40:42
Dernière modification le : dimanche 25 novembre 2018 - 01:10:41

Fichier

hodge_rank.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01932147, version 1

Collections

Citation

Pierre Lairez, Emre Can Sertöz. A numerical transcendental method in algebraic geometry. 2018. 〈hal-01932147〉

Partager

Métriques

Consultations de la notice

55

Téléchargements de fichiers

19