Totaro--Vial lemma in F-theory

TL;DR

This paper proves derived equivalences between pairs of elliptic Calabi--Yau threefolds in a specific list, revealing new relationships in their geometric structures and fibrations.

Contribution

It establishes derived equivalences for pairs of elliptic Calabi--Yau threefolds, extending the understanding of their geometric and categorical relationships.

Findings

Pairs are derived-equivalent over the base.

Most pairs produce nonbirational derived-equivalent fibrations.

One self-dual pair is an exception.

Abstract

For each pair of elliptic Calabi--Yau $3$-folds in the list of Knapp--Scieidegger--Schimannek \cite{2107.05647}, we prove that they are derived-equivalent linear over the base. Except one self-dual pair, each yields two families of smooth elliptic fibrations over a common base whose general fibers are nonbirational derived-equivalent.