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The irregularity of cyclic multiple planes after Zariski

Abstract : A formula for the irregularity of a cyclic multiple plane associated to a branch curve that has arbitrary singularities and is transverse to the line at infinity is established. The irregularity is expressed as a sum of superabundances of linear systems associated to some multiplier ideals of the branch curve and the proof rests on the theory of standard cyclic coverings. Explicit computations of multiplier ideals are performed and some applications are presented.
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https://hal.archives-ouvertes.fr/hal-00021124
Contributor : Daniel Naie <>
Submitted on : Monday, April 10, 2006 - 3:11:23 PM
Last modification on : Tuesday, April 21, 2020 - 5:00:05 PM
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Daniel Naie. The irregularity of cyclic multiple planes after Zariski. L'Enseignement Mathématique , Zürich International Mathematical Society Publishing House, 2007, 53, pp.265-305. ⟨hal-00021124v2⟩

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