Tohoku Mathematical Journal

Regular functions transversal at infinity

Alexandru Dimca and Anatoly Libgober

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We generalize and complete some of Maxim's recent results on Alexander invariants of a polynomial transversal to the hyperplane at infinity. Roughly speaking, and surprisingly, such a polynomial behaves, both topologically and algebraically (e.g., in terms of the variation of MHS on the cohomology of its smooth fibers), like a homogeneous polynomial.

Article information

Tohoku Math. J. (2), Volume 58, Number 4 (2006), 549-564.

First available in Project Euclid: 1 February 2007

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Zentralblatt MATH identifier

Primary: 32S20: Global theory of singularities; cohomological properties [See also 14E15]
Secondary: 32S22: Relations with arrangements of hyperplanes [See also 52C35] 32S35: Mixed Hodge theory of singular varieties [See also 14C30, 14D07] 32S40: Monodromy; relations with differential equations and D-modules 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 32S60: Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx] 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14J70: Hypersurfaces 14F17: Vanishing theorems [See also 32L20] 14F45: Topological properties

Hypersurface complement Alexander polynomials local system Milnor fiber perverse sheaves mixed Hodge structure


Dimca, Alexandru; Libgober, Anatoly. Regular functions transversal at infinity. Tohoku Math. J. (2) 58 (2006), no. 4, 549--564. doi:10.2748/tmj/1170347689.

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