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arXiv · 2605.29143

The quartic threefold is symplectically irrational

Jiaji Cai
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Abstract

We prove that smooth quartic threefolds are symplectically irrational: they cannot be related to projective space by a sequence of symplectic blow-ups, blow-downs, and deformations. This recovers the classical irrationality theorem of Iskovskikh-Manin. The obstruction is constructed from big quantum cohomology, using the multiplicities of eigenvalues of quantum multiplication by the Euler vector field. To prove its invariance, we establish a decomposition theorem for quantum cohomology under symplectic blow-ups, following the work of Iritani.

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Jiaji Cai. 2026-05-27. The quartic threefold is symplectically irrational. https://arxiv.org/abs/2605.29143

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