Generalized Broughton polynomials and characteristic varieties

Nguyen Tat Thang

doi:10.2478/auom-2013-0014

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Generalized Broughton polynomials and characteristic varieties

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 21 (2013): Issue 1 (March 2013)

By: Nguyen Tat Thang

Open Access

|Jul 2013

Abstract

We introduce a family of generalized Broughton polynomials and compute the characteristic varieties of complement of curve arrange- ments defined by fibers of those generalized Broughton polynomials.

References

[1] Arapura, D., Geometry of cohomology support loci for local systems. I, J. Algebraic Geom., 6 (1997), no. 3, 563-597.
Search in Google Scholar
[2] Beauville, A., Annulation du H1 pour les fibrs en droites plats, in: Complex algebraic varieties (Bayreuth, 1990), 1-15, Lecture Notes in Math., vol. 1507, Springer, Berlin, 1992.
Search in Google Scholar
[3] Broughton, S. A., Milnor numbers and the topology of polynomial hyper-surfaces, Invent. Math., 92 (1988), no. 2, 217- 241.
Search in Google Scholar
[4] Dimca, A., Singularities and Topology of Hypersurfaces, Universitext, Springer, 1992.10.1007/978-1-4612-4404-2
Search in Google Scholar
[5] Dimca, A., Sheaves in Topology, Universitext, Springer-Verlag, 2004.10.1007/978-3-642-18868-8
Search in Google Scholar
[6] Dimca, A., Characteristic varieties and constructible sheaves, Rend. Lincei Mat. Appl., 18 (2007), no. 4, 365-389.
Search in Google Scholar
[7] Dimca, A., On the irreducible components of characteristic varieties, An. Stiin. Univ. ”Ovidius” Constanta Ser. Mat. 15 (2007), no. 1, 67-73.
Search in Google Scholar
[8] Dimca, A., Papadima, S. and Suciu, A., Topology and geometry of coho-mology jump loci, Duke Math. J., 148 (2009), no. 3, 405-457.
Search in Google Scholar
[9] Green, M. and Lazarsfeld, R., Higher obstructions to deforming coho-mology groups of line bundles, J. Amer. Math. Soc., 4 (1991), no. 1, 87-103.
Search in Google Scholar
[10] H`a, H. V. and Lˆe, D. T., Sur la topologie des polyn^omes complexes, Acta Math. Vietnamica, 9 (1984), 21- 32.
Search in Google Scholar
[11] Simpson, C., Subspaces of moduli spaces of rank one local systems, Ann. Sci. Ecole Norm. Sup. 26 (1993), no. 3, 361- 401.
Search in Google Scholar
[12] Zahid, R., Broughton polynomials and characteristic varieties, Studia Sci. Math. Hungarica, 47 (2010), no.2, 214-222.
Search in Google Scholar