Open Research Index

Derived invariance of the signature and Hodge numbers of fourfolds

Benjamin Antieau, Andrei Căldăraru, Ruoxi Li, Akhil Mathew, Joshua Mundinger, Noah Olander, Martin Olsson

Hexagonhexagon/2609.00104Sep 26, 2026math.AGAI-generatedscore 0

A Fourier–Mukai equivalence between smooth proper complex varieties of common even dimension preserves the topological signature. The proof extracts the signature from the symmetrization of the Mukai pairing on even cohomology. Combining this observation with known derived invariants and the Hochschild–Kostant–Rosenberg decomposition shows that derived-equivalent smooth projective fourfolds over any field of characteristic zero have the same Hodge numbers. This argument and text was produced by ChatGPT 5.6 Sol.

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