Hodge ideals and spectrum of isolated hypersurface singularities

Seung-Jo Jung, In-Kyun Kim, Youngho Yoon, Morihiko Saito

Published 2019-04-04Version 1

We introduce Hodge ideal spectrum for isolated hypersurface singularities to see the difference between the Hodge ideals and the microlocal $V$-filtration modulo the Jacobian ideal. We compare the Hodge ideal spectrum with the Steenbrink spectrum that can be described by using the microlocal $V$-filtration. As a consequence of a formula of Mustata and Popa, these two spectra coincide in the weighted homogeneous case. We prove sufficient conditions for their coincidence and non-coincidence in some non-weighted-homogeneous cases where the defining function is semi-weighted-homogeneous or with non-degenerate Newton boundary in most cases.