New counterexamples to the birational Torelli theorem for Calabi–Yau manifolds
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- by Marco Rampazzo;
- Proc. Amer. Math. Soc. 152 (2024), 2317-2331
- DOI: https://doi.org/10.1090/proc/16745
- Published electronically: April 16, 2024
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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 $(n^2-1)$-folds which, for $n \geq 2$ 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.References
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Bibliographic Information
- Marco Rampazzo
- Affiliation: Department of Mathematics, University of Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
- MR Author ID: 1355486
- ORCID: 0000-0001-5481-9271
- Email: marco.rampazzo3@unibo.it, marco.rampazzo.90@gmail.com
- Received by editor(s): November 22, 2022
- Received by editor(s) in revised form: October 31, 2023
- Published electronically: April 16, 2024
- Additional Notes: This work was supported by PRIN2017 “2017YRA3LK” and PRIN2020 “2020KKWT53”.
- Communicated by: Jerzy Weyman
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2317-2331
- MSC (2020): Primary 14C34, 14J32, 32M10, 14M15
- DOI: https://doi.org/10.1090/proc/16745
- MathSciNet review: 4741230