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Title: 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 [Formula: see text]-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 [Formula: see text]-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.  more » « less
Award ID(s):
1945611
PAR ID:
10409083
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Communications in Contemporary Mathematics
Volume:
24
Issue:
10
ISSN:
0219-1997
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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