Title :

Reflective modular forms and their applications

Author(s) :

Gritsenko, Valery A. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut universitaire de France [IUF]

Journal title :

Usp.Mat.Nauk

Pages :

53-122

Publication date :

2018

HAL domain(s) :

Physique [physics]/Physique mathématique [math-ph]
Physique [physics]/Physique des Hautes Energies - Théorie [hep-th]

English abstract : [en]

We prove that the existence of a strongly reflective modular form of a large weight implies that the Kodaira dimension of the corresponding modular variety is negative or, in some special case, it is equal to zero. Using ...
Show more >We prove that the existence of a strongly reflective modular form of a large weight implies that the Kodaira dimension of the corresponding modular variety is negative or, in some special case, it is equal to zero. Using the Jacobi lifting we construct three towers of strongly reflective modular forms with the simplest possible divisor. In particular we obtain a Jacobi lifting construction of the Borcherds-Enriques modular form Phi_4 and Jacobi liftings of automorphic discriminants of the K\'ahler moduli of Del Pezzo surfaces constructed recently by Yoshikawa. We obtain also three modular varieties of dimension 4, 6 and 7 of Kodaira dimension 0.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL