Resonant bands, Aomoto complex, and real 4-nets

Michele Torielli and Masahiko Yoshinaga

Journal of Singularities
volume 11 (2015), 33-51

Received: 3 September 2014. Received in revised form: 3 March 2015.

DOI: 10.5427/jsing.2015.11b

Add a reference to this article to your citeulike library.


Abstract:

The resonant band is a useful notion for the computation of the nontrivial monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this article, we develop the resonant band description for the cohomology of the Aomoto complex. As an application, we prove that real 4-nets do not exist.


Author(s) information:

Michele Torielli Masahiko Yoshinaga
Department of Mathematics "Giuseppe Peano" Department of Mathematics
University of Turin Hokkaido University
Via Carlo Alberto 10 Kita 10, Nishi 8, Kita-Ku
10123, Turin, Italy Sapporo 060-0810, Japan
email: michele.torielli@unito.it email: yoshinaga@math.sci.hokudai.ac.jp