Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of the Bernstein–Sato polynomial for a direct summand of a polynomial over a field...
| Autores: | , , |
|---|---|
| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/341752 |
| Acceso en línea: | https://hdl.handle.net/2117/341752 |
| Access Level: | acceso abierto |
| Palabra clave: | Commutative algebra Àlgebra commutativa Classificació AMS::14 Algebraic geometry::14F (Co)homology theory Classificació AMS::13 Commutative rings and algebras::13N Differential algebra Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of the Bernstein–Sato polynomial for a direct summand of a polynomial over a field is proved in this context. It is observed that this polynomial can have zero as a root, or even positive roots. Moreover, a theory of V -filtrations is introduced for nonregular rings, and the existence of these objects is established for what we call differentially extensible summands. This family of rings includes toric, determinantal, and other invariant rings. This new theory is applied to the study of multiplier ideals and Hodge ideals of singular varieties. Finally, we extend known relations among the objects of interest in the smooth case to the setting of singular direct summands of polynomial rings. |
|---|