Statut |
Confirmé |
Série |
SEM-DARBOUX |
Domaines |
hep-th,math |
Date |
Jeudi 16 Janvier 2020 |
Heure |
11:00 |
Institut |
LPTHE |
Salle |
bibliothèque du LPTHE, tour 13-14, 4eme étage |
Nom de l'orateur |
Freixas Montplet |
Prenom de l'orateur |
Gerard |
Addresse email de l'orateur |
gerard [dot] freixas [at] imj-prg [dot] fr |
Institution de l'orateur |
IMJ |
Titre |
On genus one mirror symmetry |
Résumé |
Classical genus zero proposes a duality phenomenon for Calabi-Yau (CY) manifolds, relating
the Yukawa coupling for a large structure limit of CY's and enumerative invariants of rational
curves on a mirror CY. For the higher genus counting problem, the corresponding conjectural
program was proposed by Bershadsky-Cecotti-Ooguri-Vafa (BCOV). In particular, they predict
that a combination of holomorphic analytic torsions of large structure limits of CY's
encapsulate genus one enumerative invariants on a mirror. In this talk I would like to present
and discuss a refined conjecture which bypasses spectral theory and pertains to the realm of
complex geometry, as for the Yukawa coupling. I will then explain a proof of this conjecture for
the mirror family of Calabi-Yau hypersurfaces in projective space, which relies on the
arithmetic Riemann-Roch theorem in Arakelov geometry. The result is compatible with the
BCOV predictions, as well as related work by Zinger. |
Numéro de preprint arXiv |
|
Commentaires |
|
Fichiers attachés |
- Darboux-Freixas.pdf (391754 bytes)
|