Exotic Deformations of Calabi-Yau Manifolds
Annales de l'Institut Fourier, Volume 63 (2013) no. 2, p. 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 : https://doi.org/10.5802/aif.2764
Classification:  32G05,  53C15,  17B30
Keywords: tamed symplectic structure, Calabi-Yau manifold, quantum inner state structure, deformation, moduli space
@article{AIF_2013__63_2_391_0,
     author = {de Bartolomeis, Paolo and Tomassini, Adriano},
     title = {Exotic Deformations of Calabi-Yau Manifolds},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {2},
     year = {2013},
     pages = {391-415},
     doi = {10.5802/aif.2764},
     mrnumber = {3112516},
     zbl = {1293.32016},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2013__63_2_391_0}
}
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/item/AIF_2013__63_2_391_0/

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