Tohoku Mathematical Journal
2006
December
SECOND SERIES VOL. 58, NO. 4

Tohoku Math. J.
58 (2006), 549-564

Title REGULAR FUNCTIONS TRANSVERSAL AT INFINITY

Author Alexandru Dimca and Anatoly Libgober

(Received April 18, 2005, revised November 14, 2005)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 32S20; Secondary 32S22, 32S35, 32S40, 32S55, 32S60, 14D05, 14J70, 14F17, 14F45.
Key words and phrases. Hypersurface complement, Alexander polynomials, local system, Milnor fiber, perverse sheaves, mixed Hodge structure.

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