5 papers
Pure subrings of Du Bois singularities are Du Bois singularities
Charles Godfrey, Takumi Murayama
Let be a cyclically pure map of Noetherian -algebras. In this paper, we show that if has Du Bois singularities, then has Du Bois singularities. Our re…
Equidimensional morphisms onto splinters are pure
Takumi Murayama
We prove that a Noetherian ring is a splinter if and only if for every equidimensional surjective morphism , the map $R \to S…
Moving Seshadri constants and effective Fujita-type conjectures
Takumi Murayama
Fujita's conjecture is known to be false in positive characteristic. We conjecture and give an approach to a new variant of Fujita's conjecture for the basepoint-freeness, very amp…
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero
Shiji Lyu, Takumi Murayama
We establish the relative minimal model program with scaling for locally projective morphisms of quasi-excellent algebraic spaces admitting dualizing complexes, quasi-excellent for…
Finiteness of associated primes for local cohomology modules of excellent locally unramified regular rings of finite Krull dimension
Takumi Murayama
Thirty years ago, Huneke (for local rings) and Lyubeznik (in general) conjectured that for all regular rings , the local cohomology modules have finitely many associa…