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Line arrangements in topological, smooth, and symplectic categories Starkston, Laura


A complex line arrangement is a collection of complex projective lines in \(CP^2\) which may intersect at points of multiplicity greater than two. The combinatorial arrangements which can be geometrically realized and their space of realizations have been studied classically. We define symplectic, smooth, and topological versions of complex line arrangements in \(CP^2\), and study their realizability. While one might hope that these more flexible categories allow us to realize any combinatorics, in fact we show that there are obstructions to topological realizations of many combinatorial arrangements. Many open questions remain about realizability in different categories.

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