2019/07/23 by Josep Álvarez Montaner, Daniel J. Hernández, Montaner, Josep Àlvarez +9 · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1907.10017
openalex publication_date 2019/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates the existence and properties of a Bernstein-Sato\nfunctional equation in nonregular settings. In particular, we construct\nD-modules in which such formal equations can be studied. The existence of the\nBernstein-Sato polynomial for a direct summand of a polynomial over a field is\nproved in this context. It is observed that this polynomial can have zero as a\nroot, or even positive roots. Moreover, a theory of V-filtrations is\nintroduced for nonregular rings, and the existence of these objects is\nestablished for what we call differentially extensible summands. This family of\nrings includes toric, determinantal, and other invariant rings. This new theory\nis applied to the study of multiplier ideals and Hodge ideals of singular\nvarieties. Finally, we extend known relations among the objects of interest in\nthe smooth case to the setting of singular direct summands of polynomial rings.\n