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Abstract: We show that the monodromy operator action on the first cohomology group of the Milnor fiber is combinatorially determined for line arrangements with at most triple points and containing at ...
Generalized Lantern Relations and Planar Line Arrangements
Generalized Lantern Relations Planar Line Arrangements Geometric Topology
2011/8/24
Abstract: In this paper we show that to each planar line arrangement defined over the real numbers, for which no two lines are parallel, one can write down a corresponding relation on Dehn twists that...
Line arrangements and direct sums of free groups
Line arrangements direct sums of free groups
2010/12/13
We show that if the fundamental groups of the complements of two line arrangements in the complex projective plane are isomorphic to the same direct sum of free groups, then the complements of the arr...
On the connectivity of the realization spaces of line arrangements
realization spaces of line arrangements
2010/11/26
We prove that under certain combinatorial conditions, the realization spaces of line arrangements on the complex projective plane are connected. We also give several examples of arrangements with eigh...