5 papers
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…
A counterexample to the PIA conjecture for minimal log discrepancies
Yusuke Nakamura, Kohsuke Shibata
We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.
Inversion of adjunction for quotient singularities III: semi-invariant case
Yusuke Nakamura, Kohsuke Shibata
We prove the precise inversion of adjunction formula for finite linear group quotients of complete intersection varieties defined by semi-invariant equations. As an application, we…
-rationality of two-dimensional graded rings with a rational singularity
Kohsuke Shibata
It is known that a two-dimensional -rational ring has a rational singularity. However a two-dimensional ring with a rational singularity is not -rational in general. In this…
A characterization of binomial Macaulay dual generators for complete intersections
Kohsuke Shibata
We characterize a binomial such that the Artinian algebra whose Macaulay dual generator is the binomial is a complete intersection. As an application, we prove that the Artinian al…