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To any graph and smooth algebraic curve C, one may associate a “hypercurve” arrangement, and one can study the rational homotopy theory of the complement X. In the rational case (C = C), there is considerable literature on the rational homotopy theory of X, and the trigonometric case (C D C ) is similar in flavor. The case when C 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 X, and we prove that X is rationally K(π, 1). x

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Algebraic and Geometric Topology

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