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math.AG2026
A non-klt counterexample to Shokurov's index conjecture
Yusuke Nakamura, Kohsuke Shibata
We give a counterexample to Shokurov's index conjecture for minimal log discrepancies in the non-klt setting.
math.AG2026
A characterization of virtually free actions via arc spaces and its application to the lower semi-continuity conjecture
Yusuke Nakamura, Kohsuke Shibata
In this paper, we study the precise inversion of adjunction (PIA) conjecture and the lower semi-continuity (LSC) conjecture for hyperquotient singularities. Previously known result…