New counterexamples to the birational Torelli theorem for Calabi--Yau manifolds

2022/11/07 by Rampazzo, Marco · 1 citation
#14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.03702

Abstract

We produce counterexamples to the birational Torelli theorem for Calabi-Yau manifolds in arbitrarily high dimension: this is done by exhibiting a series of non birational pairs of Calabi-Yau (n²-1)-folds which, for n ≥ 2 even, admit an isometry between their middle cohomologies. These varieties also satisfy an \mathbb L-equivalence relation in the Grothendieck ring of varieties, i.e. the difference of their classes annihilates a power of the class of the affine line. We state this last property for a broader class of Calabi-Yau pairs, namely all those which are realized as pushforwards of a general (1,1)-section on a homogeneous roof in the sense of Kanemitsu, along its two extremal contractions.

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