A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers

2026/07/21 by Matthew Satriano, Jeremy Usatine
#math.AG

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Abstract

Batyrev's conjecture on the non-negativity of stringy Hodge numbers has been a fundamental open problem, guiding and motivating many beautiful mathematical results in motivic integration, mirror symmetry, and the McKay correspondence. We give a counter-example to Batyrev's conjecture which was discovered with the assistance of OpenAI's ChatGPT.

Related

• Stringy Hodge numbers and p-adic Hodge theory
• Strong McKay Correspondence, String-theoretic Hodge Numbers and Mirror Symmetry
• On the nonnegativity of stringy Hodge numbers
• A Counter Example To the Hodge Conjecture
• Stringy Hodge numbers of strictly canonical nondegenerate singularities