Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T01:20:09.302Z Has data issue: false hasContentIssue false
  • English
  • Français

The Poincaré–Deligne Polynomial of Milnor Fibers of Triple Point Line Arrangements is Combinatorially Determined

Published online by Cambridge University Press:  20 November 2018

Alexandru Dimca
Alexandru Dimca*
Affiliation:
Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using a recent result by S. Papadima and A. Suciu, we show that the equivariant Poincaré– Deligne polynomial of the Milnor fiber of a projective line arrangement having only double and triple points is combinatorially determined.

Keywords

32S2232S3532S2532S55line arrangementMilnor fibermonodromymixed Hodge structures
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 2 , 01 June 2016 , pp. 279 - 286
Copyright
Copyright © Canadian Mathematical Society 2016

References

[1] Bailet, P., Arrangement d'hyperplanes. PhD thesis, Univ. Nice Sophia Antipolis, 2014.Google Scholar
[2] Budur, N. and Saito, M., Jumping coefficients and spectrum of a hyperplane arrangement.Math. Ann. 347(2010), no. 3, 545–579. http://dx.doi.org/10.1007/s00208-009-0449-y Google Scholar
[3] Budur, N., Dimca, A., and Saito, M., First Milnor cohomology of hyperplane arrangements.In: Topology of algebraic varieties and singularities, Contemp. Math., 538, American Mathematical Society, Providence, RI, 2011, pp. 279–292. http://dx.doi.org/10.1090/conm/538/10606 Google Scholar
[4] Cohen, D. C. and Suciu, A. I., On Milnor fibrations of arrangements.J. London Math. Soc. 51(1995), no. 1, 105–119. http://dx.doi.org/10.1112/jlms/51.1.105 Google Scholar
[5] Dimca, A., Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements. NagoyaMath. J. 206(2012), 75–97. http://dx.doi.org/10.1215/00277630-1548502 Google Scholar
[6] Dimca, A., Monodromy of triple point line arrangements. In: Singularities in Geometry and Topology 2011, Adv. Studies in Pure Math., 66, Math. Soc. Japan, Tokyo, 2015, pp. 71–80.Google Scholar
[7] Dimca, A. and Lehrer, G., Hodge-Deligneequivariant polynomials and monodromy of hyperplane arrangements. In: Configuration spaces, CRM Series, 14, Ed. Norm., Pisa, 2012, pp. 231–253.http://dx.doi.org/10.1007/978-88-7642-431-1J0 Google Scholar
[8] Dimca, A. and Lehrer, G., On the cohomology of the Milnor fibre of a hyperplane arrangement. arxiv:1307.3847Google Scholar
[9] Dimca, A. and Papadima, S., Finite Galois covers, cohomology jump loci, formality properties, and multinets. Ann. Sc. Norm. Super. Pisa Cl. Sci(5) 10(2011), no. 2, 253–268.Google Scholar
[10] Dimca, A. and Saito, M., Some remarks on limit mixed Hodge structure and spectrum. An. St. Univ. Ovidius Constanta Ser. Mat. 22(2014), no. 2, 69–78.Google Scholar
[11] Esnault, H., Fibrede Milnor d'un cône sur une courbe plane singulière. Invent. Math. 68(1982), no. 3, 477–496. http://dx.doi.org/10.1007/BF01389413 Google Scholar
[12] Libgober, A., Hodge decomposition of Alexander invariants.Manuscripta Math. 107(2002), no. 2, 251–269. http://dx.doi.org/10.1007/s002290100243 Google Scholar
[13] Libgober, A., Eigenvalues for the monodromyof the Milnor fibers of arrangements. In: Trends in singularities, Trends Math., Birkhâuser, Basel, 2002, pp. 141–150.Google Scholar
[14] Loeser, F. and Vaquie, M., Le polynôme dAlexanderd'une courbe plane projective.Topology 29(1990), 163–173. http://dx.doi.org/10.1 01 6/0040-9383(90)90005-5 Google Scholar
[15] Papadima, S. and Suciu, A. I., The Milnor fibration of a hyperplane arrangement: from modular resonance to algebraic monodromy. arxiv:1401.08680.Google Scholar
[16] Peters, C. and Steenbrink, J., Mixed Hodge structures. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3, Series of Modern Surveys in Mathematics, 52, Springer-Verlag, Berlin, 2008.Google Scholar
[17] Orlik, P. and Terao, H., Arrangements of hyperplanes.Grundlehren der Mathematischen Wissenschaften, 300, Springer-Verlag, Berlin, 1992.http://dx.doi.org/10.1007/978-3-662-02772-1 Google Scholar
[18] Steenbrink, J., Intersection form for quasi-homogeneous singularities.Compositio Math. 34(1977), no. 2, 211–223.Google Scholar