2 problems

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Gongyo's log-canonicity conjecture for ramification divisors
Gongyo's conjecture. After replacing $f$ by an iterate, the pair
Conjecturesolvedlog-canonical-pairs polarized-endomorphisms ramification-divisorsarXiv posted 2 days ago
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Rank conjecture for the restricted ramification divisor map
Rank conjecture. The rank of the complex derivative of $\rho$ at $(i_1,i_2)$ satisfies:
Conjectureopencone-spherical-metrics ramification-divisors riemann-surfacesarXiv posted 2 days ago

Gongyo's log-canonicity conjecture for ramification divisors