We explore the relation between cohomology jump loci in a finite Galois cover, formality properties and algebraic monodromy action. We show that the jump loci of the base and total space are essentially the same, provided the base space is 1-formal and the monodromy action in degree 1 is trivial. We use reduced multinet structures on line arrangements to construct components of the first characteristic variety of the Milnor fiber in degree 1, and to prove that the monodromy action is non-trivial in degree 1. For an arbitrary line arrangement, we prove that the triviality of the monodromy in degree 1 can be detected in a precise way, by resonance varieties.
@article{ASNSP_2011_5_10_2_253_0,
author = {Dimca, Alexandru and Papadima, Stefan},
title = {Finite {Galois} covers, cohomology jump loci, formality properties, and multinets},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {253--268},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 10},
number = {2},
year = {2011},
mrnumber = {2856148},
zbl = {1239.32023},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2011_5_10_2_253_0/}
}
TY - JOUR AU - Dimca, Alexandru AU - Papadima, Stefan TI - Finite Galois covers, cohomology jump loci, formality properties, and multinets JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 253 EP - 268 VL - 10 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_2_253_0/ LA - en ID - ASNSP_2011_5_10_2_253_0 ER -
%0 Journal Article %A Dimca, Alexandru %A Papadima, Stefan %T Finite Galois covers, cohomology jump loci, formality properties, and multinets %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 253-268 %V 10 %N 2 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2011_5_10_2_253_0/ %G en %F ASNSP_2011_5_10_2_253_0
Dimca, Alexandru; Papadima, Stefan. Finite Galois covers, cohomology jump loci, formality properties, and multinets. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 2, pp. 253-268. http://www.numdam.org/item/ASNSP_2011_5_10_2_253_0/
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