Hodge ideals and microlocal V-filtration

Abstract

We show that the Hodge ideals in the sense of Mustata and Popa are quite closely related to the induced microlocal V-filtration on the structure sheaf, defined by using the microlocalization of the V-filtration of Kashiwara and Malgrange. More precisely the former coincide, module the ideal of the divisor, with the part of the latter indexed by positive integers, although they are different without modulo the ideal in general. This coincidence implies that the $j$-log-canonicity in their sense is determined by the microlocal log-canonical threshold of the divisor, which coincides with the maximal root of the reduced (or microlocal) Bernstein-Sato polynomial up to a sign.

arXiv comment19 pages

Cited by in corpus (8)

• Hodge ideals for Q-divisors, V-filtration, and minimal exponent
• On singularity properties of convolutions of algebraic morphisms -- the general case (with an appendix joint with Gady Kozma)
• Hodge filtration and Hodge ideals for $\mathbb{Q}$-divisors with weighted homogeneous isolated singularities
• Hodge ideals and minimal exponents of ideals
• Hodge ideals for Q-divisors: birational approach
• Deformations of Calabi-Yau varieties with $k$-liminal singularities
• Descent of nearby cycle formula for Newton non-degenerate functions
• D-modules in birational geometry