Exotic Deformations of Calabi-Yau Manifolds

de Bartolomeis, Paolo; Tomassini, Adriano

doi:10.5802/aif.2764

Exotic Deformations of Calabi-Yau Manifolds
[Déformations exotiques des variétés de Calabi-Yau]

de Bartolomeis, Paolo ¹ ; Tomassini, Adriano ²

¹ Università di Firenze Dipartimento di Matematica e Informatica “Ulisse Dini” Viale Morgagni 67/a 50134 Firenze (Italy)
² Università di Parma Dipartimento di Matematica e Informatica Parco Area delle Scienze 53/A 43124 Parma (Italy)

Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 391-415.

Résumé
Abstract

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

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

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

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

MR Zbl

DOI : 10.5802/aif.2764

Classification : 32G05, 53C15, 17B30
Keywords: tamed symplectic structure, Calabi-Yau manifold, quantum inner state structure, deformation, moduli space
Mot clés : variétés de Calabi-Yau

Affiliations des auteurs :

de Bartolomeis, Paolo ¹ ; Tomassini, Adriano ²

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     title = {Exotic {Deformations} of {Calabi-Yau} {Manifolds}},
     journal = {Annales de l'Institut Fourier},
     pages = {391--415},
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de Bartolomeis, Paolo; Tomassini, Adriano. Exotic Deformations of Calabi-Yau Manifolds. Annales de l'Institut Fourier, Tome 63 (2013) no. 2, pp. 391-415. doi : 10.5802/aif.2764. https://www.numdam.org/articles/10.5802/aif.2764/

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