Exotic Deformations of Calabi-Yau Manifolds

[Déformations exotiques des variétés de Calabi-Yau]

de Bartolomeis, Paolo ; Tomassini, Adriano

Annales de l'Institut Fourier, Tome 63 (2013), p. 391-415 / Harvested from Numdam

Résumé

On considère la classe des variétés QIS (Quantum Inner State variétés), à savoir la classe des variétés symplectiques, compactes et de dimension $2n$, munies d’une structure presque complexe $J$ modérée par $k$ et d’une section $\epsilon $ du fibré $\Lambda ^{n,0}_J(M)$, qui ne s’annule nulle part, normalisée et satisfaisant la condition $\overline{\partial }_J\epsilon =0$.

Le but du papier est d’étudier l’espace $\mathfrak{M}$ des modules des déformations QIS d’une variété de Calabi-Yau. À ce propos, on calcule l’espace tangent de $\mathfrak{M}$ et on montre que $\mathfrak{M}$ n’a pas d’obstructions. Plusieurs exemples de variétés QIS sont aussi exhibés.

Abstract

We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) $2n$-dimensional symplectic manifolds $(M,\kappa )$ endowed with a $\kappa $-tamed almost complex structure $J$ and with a nowhere vanishing and normalized section $\epsilon $ of the bundle $\Lambda ^{n,0}_J(M)$ satisfying the condition $\overline{\partial }_J\epsilon =0$.

We study the moduli space $\mathfrak{M}$ of QIS deformations of a given Calabi-Yau manifold, computing its tangent space and showing that $\mathfrak{M}$ is non obstructed. Finally, we present several examples of QIS manifolds.

Détail

Publié le : 2013-01-01

MR 3112516 | Zbl 1293.32016

DOI : https://doi.org/10.5802/aif.2764
Classification:  32G05,  53C15,  17B30
Mots clés: variétés de Calabi-Yau

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