Bernstein-Sato functional equations, $V$-filtrations, and multiplier ideals of direct summands
| Autor: | Daniel J. Hernández, Emily E. Witt, Pedro Teixeira, Luis Núñez-Betancourt, Josep Àlvarez Montaner, Jack Jeffries |
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| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
16 Associative rings and algebras::16S Rings and algebras arising under various constructions [Classificació AMS] Rings (Algebra) General Mathematics Commutative rings Bernstein–Sato polynomial Multiplier ideal Anells commutatius Commutative Algebra (math.AC) Multiplier (Fourier analysis) Mathematics - Algebraic Geometry Functional equation FOS: Mathematics 13 Commutative rings and algebras::13A General commutative ring theory [Classificació AMS] D-module Ring of invariants Algebraic Geometry (math.AG) Mathematics V -filtrations 14 Algebraic geometry::14F (Co)homology theory [Classificació AMS] Direct summand Mathematics::Commutative Algebra Applied Mathematics Construct (python library) Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC] Mathematics - Commutative Algebra 13 Commutative rings and algebras::13N Differential algebra [Classificació AMS] Anells (Àlgebra) |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | 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. 42 pages. A new section on Hodge ideals is included. Comments welcome |
| Databáze: | OpenAIRE |
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