Exotic Deformations of Calabi-Yau Manifolds
Annales de l'Institut Fourier, Volume 63 (2013) no. 2, pp. 391-415.

We introduce Quantum Inner State manifolds (QIS manifolds) as (compact) 2n-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 ¯ 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.

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 ϵ du fibré Λ J n,0 (M), qui ne s’annule nulle part, normalisée et satisfaisant la condition ¯ 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.

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
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)
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de Bartolomeis, Paolo; Tomassini, Adriano. Exotic Deformations of Calabi-Yau Manifolds. Annales de l'Institut Fourier, Volume 63 (2013) no. 2, pp. 391-415. doi : 10.5802/aif.2764. http://www.numdam.org/articles/10.5802/aif.2764/

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