Hodge ideals of free divisors

• Alberto Castaño Domínguez ^[1] ; Luis Narváez Macarro ^[1] ; Christian Sevenheck ^[2]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
  2. [2] Chemnitz University of Technology

     Chemnitz University of Technology

     Kreisfreie Stadt Chemnitz, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 3, 2022
• Idioma: inglés
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• Resumen

  • 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.