8 citations · 11 across the 11 of their papers we have counts for
13 papers
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.
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 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…
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…
Shokurov's index conjecture for quotient singularities
Yusuke Nakamura, Kohsuke Shibata
We prove Shokurov's index conjecture for quotient singularities.
Inversion of adjunction for quotient singularities II: Non-linear actions
Yusuke Nakamura, Kohsuke Shibata
We prove the precise inversion of adjunction formula for quotient singularities. As an application, we prove the semi-continuity of minimal log discrepancies for hyperquotient sing…
-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…
Inversion of adjunction for quotient singularities
Yusuke Nakamura, Kohsuke Shibata
We prove the precise inversion of adjunction formula for quotient singularities and klt Cartier divisors. As an application, we prove the semi-continuity of minimal log discrepanci…
Characterization of two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic
Kohsuke Shibata
In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an ap…
Minimal log discrepancies in positive characteristic
Kohsuke Shibata
We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of mini…
Bounds of the multiplicity of abelian quotient complete intersection singularities
Kohsuke Shibata
In this paper, we investigate the multiplicities and the log canonical thresholds of abelian quotient complete intersection singularities in term of the special datum. Moreover we…
The core of a module and the adjoint of an ideal over a two dimensional regular local ring
Kohsuke Shibata
The core of an module is the intersection of all its reductions. The main result asserts that the core of a finitely generated, torsion-free, integrally closed module over a two di…