Higher multiplier ideals are introduced as a two-parameter family of ideal sheaves via mixed Hodge modules, with vanishing/restriction theorems proved and new cases of theta divisor conjectures established.
Hodge ideals and microlocal V-filtration
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
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UNVERDICTED 2representative citing papers
Missing spectral numbers between Steenbrink and Tjurina spectra for hypersurface singularities exhibit canonical graded symmetry from Jacobian ring self-duality.
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Higher multiplier ideals
Higher multiplier ideals are introduced as a two-parameter family of ideal sheaves via mixed Hodge modules, with vanishing/restriction theorems proved and new cases of theta divisor conjectures established.
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Tjurina spectrum and graded symmetry of missing spectral numbers
Missing spectral numbers between Steenbrink and Tjurina spectra for hypersurface singularities exhibit canonical graded symmetry from Jacobian ring self-duality.