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arXiv · 2611.01716

Derived Torelli for Kuznetsov components of cubic fourfolds

Hanfei Guo·Ruxuan Zhang
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Abstract

We prove that every orientation-preserving Hodge isometry between the integral Mukai lattices of the Kuznetsov components of two smooth cubic fourfolds is induced by an exact equivalence. The proof uses Markman--Mehrotra's comonad reconstruction method to recover both Kuznetsov components from a common Fourier--Mukai comonad on a moduli space of stable objects. As an application, we prove that the Kuznetsov components of two smooth cubic fourfolds are equivalent whenever their Fano varieties of lines are derived equivalent.

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Hanfei Guo, Ruxuan Zhang. 2026-11-01. Derived Torelli for Kuznetsov components of cubic fourfolds. https://arxiv.org/abs/2611.01716

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