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Non-birational Calabi-Yau threefolds that are derived equivalent

Andrei Caldararu
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Abstract

We argue that the existence of genus one fibrations with multisections of high degree on certain Calabi-Yau threefolds implies the existence of pairs of such varieties that are not birational, but are derived equivalent. It also (likely) implies the existence of non-birational counterexamples to the Torelli problem for Calabi-Yau threefolds.

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Andrei Caldararu. 2006-06-22. Non-birational Calabi-Yau threefolds that are derived equivalent. https://arxiv.org/abs/math/0601232

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