
TL;DR
This paper presents examples of complex cubic curve arrangements with monodromy eigenvalues of order 5 and 6, revealing unexpected behaviors in curve arrangements close to line arrangements.
Contribution
It introduces specific cubic curve arrangements exhibiting non-trivial monodromy eigenvalues, expanding understanding beyond line arrangements.
Findings
Monodromy eigenvalues of order 5 and 6 in cubic arrangements
Examples close to line arrangements with complex monodromy behavior
Use of Dimca and Sticlaru's algorithm for detection
Abstract
We give two examples of plane curve arrangements of pencil type which are very close to line arrangements, though the action of the monodromy operator on the first cohomology group of the Milnor Fiber has eigenvalues of order 5 and 6, showing that surprising situations can occur for larger classes of curve arrangements than for line arrangements. Our computations rely on the algorithm given by A. Dimca and G. Sticlaru which detects the non trivial monodromy eigenspaces of free curves.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Mathematics and Applications
