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Hodge ideals of free divisors

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arxiv 1912.09786 v4 pith:BARY5RJC submitted 2019-12-20 math.AG math.CV

Hodge ideals of free divisors

Alberto Casta\~no Dom\'inguez , Luis Narv\'aez Macarro , Christian Sevenheck This is my paper
classification math.AG math.CV
keywords hodgefiltrationdivisorsfreeidealsalgorithmalongapply
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We consider the Hodge filtration on the sheaf of meromorphic functions along free divisors for which the logarithmic comparison theorem holds. We describe the Hodge filtration steps as submodules of the order filtration on a cyclic presentation in terms of a special factor of the Bernstein-Sato polynomial of the divisor and we conjecture a bound for the generating level of the Hodge filtration. Finally, we develop an algorithm to compute Hodge ideals of such divisors and we apply it to some examples.

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