Moraga’s odd-dimensional automorphism-rank bound
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Does Moraga’s proposed odd-dimensional extension bound the rank of faithful elementary-abelian group actions? The test is the Fermat quintic Calabi–Yau threefold, with faithful (μ₅)⁵/Δ action of rank four, exceeding 15/4.
Why it matters and what counts as progress
Why it matters: It tests whether the proposed rank bound survives already on a smooth explicit Calabi–Yau threefold.
What counts as progress: A faithful finite-group action exceeding the proposed odd-dimensional rank bound, or a corrected bound with the missing hypotheses.
How the problem developed
- 2024 · Conjecture [1]
János Kollár and Ziquan Zhuang, recording a conjectural extension by Moraga Established rank bounds for faithful abelian p-group actions under specified Euler-characteristic hypotheses and recorded Moraga’s proposed odd-dimensional extension, outside the cases covered by their theorem.
- 6 Jul 2026 · Counterexample [2]
Jihao Liu and Yanze Wang; the paper credits ChatGPT 5.5 Pro and Danus based on Rethlas with obtaining the main result Exhibited a faithful rank-four elementary abelian 5-group action on the Fermat quintic threefold, violating the conjectured odd-dimensional bound.
AI contribution
A counterexample to the odd-dimensional rank bound for abelian p-group actions
The smooth Fermat quintic Calabi–Yau threefold has a faithful action of (μ₅)⁵/Δ, an elementary abelian 5-group of rank four. Since 4>15/4, this refutes Moraga’s proposed odd-dimensional extension of a rank bound.
Sources
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Publication dates and editorial changes.
AI-led Fermat-quintic example refutes an odd-dimensional rank conjecture