Exotic Deformations of Calabi-Yau Manifolds

Paolo de Bartolomeis[1]; Adriano Tomassini[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 (2013)

  • Volume: 63, Issue: 2, page 391-415
  • ISSN: 0373-0956

Abstract

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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 ∂ ¯ 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.

How to cite

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de Bartolomeis, Paolo, and Tomassini, Adriano. "Exotic Deformations of Calabi-Yau Manifolds." Annales de l’institut Fourier 63.2 (2013): 391-415. <http://eudml.org/doc/275436>.

@article{deBartolomeis2013,
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.},
affiliation = {Università di Firenze Dipartimento di Matematica e Informatica “Ulisse Dini” Viale Morgagni 67/a 50134 Firenze (Italy); Università di Parma Dipartimento di Matematica e Informatica Parco Area delle Scienze 53/A 43124 Parma (Italy)},
author = {de Bartolomeis, Paolo, Tomassini, Adriano},
journal = {Annales de l’institut Fourier},
keywords = {tamed symplectic structure; Calabi-Yau manifold; quantum inner state structure; deformation; moduli space; Calabi Yau manifold},
language = {eng},
number = {2},
pages = {391-415},
publisher = {Association des Annales de l’institut Fourier},
title = {Exotic Deformations of Calabi-Yau Manifolds},
url = {http://eudml.org/doc/275436},
volume = {63},
year = {2013},
}

TY - JOUR
AU - de Bartolomeis, Paolo
AU - Tomassini, Adriano
TI - Exotic Deformations of Calabi-Yau Manifolds
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 2
SP - 391
EP - 415
AB - 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.
LA - eng
KW - tamed symplectic structure; Calabi-Yau manifold; quantum inner state structure; deformation; moduli space; Calabi Yau manifold
UR - http://eudml.org/doc/275436
ER -

References

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