Gongyo's log-canonicity conjecture for ramification divisors
Gongyo's log-canonicity conjecture for ramification divisors
Let be a smooth projective variety and let be a -polarized endomorphism, meaning that for some ample divisor and integer . Let be the ramification divisor defined by
Gongyo's conjecture. After replacing by an iterate, the pair
is log canonical. The conjecture is known in dimension two except possibly when and the sum of all -periodic prime divisors is zero; its general status is open.
Sources & referencesView supporting material
Primary source
Wentao Chang and De-Qi Zhang, “Log Calabi-Yau structure of algebaic varieties admitting a polarized endomorphism”, arXiv:2509.17927 (2025).
Additional references
3 papers in this index state this conjecture (2022–2025). The statement above is taken from the most recent of them; the others are arXiv:2311.16369, arXiv:2204.11244.
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