SYZ mirror conjecture predicts that a Calabi–Yau manifold X consists of a family of tori which are dual to a family of special Lagrangian tori on the mirror dual manifold . Here we consider a fibration of polarized abelian varieties and we construct a dual one. Moreover we prove that they are equivalent at the level of derived categories.
La conjecture de « symétrie miroir SYZ » prédit quʼune variété de Calabi–Yau X consiste en une famille de tores qui sont duaux dʼune famille de tores lagrangiennes spéciaux dans la variété miroir duale . Nous considérons ici une fibration de variétés abéliennes polarisées et nous en construisons la duale. De plus, nous montrons quʼelles sont équivalentes au niveau des catégories dérivées.
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@article{CRMATH_2012__350_13-14_689_0, author = {Mart{\'\i}nez, Cristina}, title = {Abelian fibrations and {SYZ} mirror conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {689--692}, publisher = {Elsevier}, volume = {350}, number = {13-14}, year = {2012}, doi = {10.1016/j.crma.2012.07.011}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.07.011/} }
TY - JOUR AU - Martínez, Cristina TI - Abelian fibrations and SYZ mirror conjecture JO - Comptes Rendus. Mathématique PY - 2012 SP - 689 EP - 692 VL - 350 IS - 13-14 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.07.011/ DO - 10.1016/j.crma.2012.07.011 LA - en ID - CRMATH_2012__350_13-14_689_0 ER -
%0 Journal Article %A Martínez, Cristina %T Abelian fibrations and SYZ mirror conjecture %J Comptes Rendus. Mathématique %D 2012 %P 689-692 %V 350 %N 13-14 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.07.011/ %R 10.1016/j.crma.2012.07.011 %G en %F CRMATH_2012__350_13-14_689_0
Martínez, Cristina. Abelian fibrations and SYZ mirror conjecture. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 689-692. doi : 10.1016/j.crma.2012.07.011. http://archive.numdam.org/articles/10.1016/j.crma.2012.07.011/
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