Abstract
To any graph and smooth algebraic curve , one may associate a “hypercurve” arrangement, and one can study the rational homotopy theory of the complement . In the rational case (), there is considerable literature on the rational homotopy theory of , and the trigonometric case () is similar in flavor. The case when is a smooth projective curve of positive genus is more complicated due to the lack of formality of the complement. When the graph is chordal, we use quadratic-linear duality to compute the Malcev Lie algebra and the minimal model of , and we prove that is rationally .
Citation
Christin Bibby. Justin Hilburn. "Quadratic-linear duality and rational homotopy theory of chordal arrangements." Algebr. Geom. Topol. 16 (5) 2637 - 2661, 2016. https://doi.org/10.2140/agt.2016.16.2637
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