Abstract
This is a short note on the study of cohomology groups of rank one local systems of real line arrangements via resonant bands. Results on Milnor fibers and several conjectures are also stated.
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References
Cohen, D., Dimca, A., Orlik, P.: Nonresonance conditions for arrangements. Ann. Inst. Fourier 53, 1883–1896 (2003)
Cohen, D., Suciu, A.: On Milnor fibrations of arrangements. J. Lond. Math. Soc. 51(2), 105–119 (1995)
Falk, M., Yuzvinsky, S.: Multinets, resonance varieties, and pencils of plane curves. Compos. Math. 143(4), 1069–1088 (2007)
Grünbaum, B.: A catalogue of simplicial arrangements in the real projective plane. Ars Math. Contemp. 2(1), 1–25 (2009)
Libgober, A.: Eigenvalues for the monodromy of the Milnor fibers of arrangements. In: Trends in Singularities. Trends in Mathematics, pp. 141–150. Birkhäuser, Basel (2002)
Suciu, A.: Fundamental groups of line arrangements: enumerative aspects. In: Advances in Algebraic Geometry Motivated by Physics (Lowell, MA, 2000). Contemporary Mathematics, vol. 276, pp. 43–79. American Mathematical Society, Providence (2001)
Suciu, A.: Hyperplane arrangements and Milnor fibrations. Ann. Fac. Sci. Toulouse Math. 23(2), 417–481 (2014)
Yoshinaga, M.: Milnor fibers of real line arrangements. J. Singularities 7, 220–237 (2013)
Yoshinaga, M.: Resonant bands and local system cohomology groups for real line arrangements. Vietnam Jour. Math. 42(3), 377–392 (2014)
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Yoshinaga, M. (2015). Resonant Bands, Local Systems and Milnor Fibers of Real Line Arrangements. In: Benedetti, B., Delucchi, E., Moci, L. (eds) Combinatorial Methods in Topology and Algebra. Springer INdAM Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-20155-9_25
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DOI: https://doi.org/10.1007/978-3-319-20155-9_25
Publisher Name: Springer, Cham
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