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While arrangements of hyperplanes have been studied in algebra, combinatorics and geometry for a long time, recent discoveries suggest that they (and more generally arrangements of nonlinear subvarieties) play an even more fundamental role in major problems in algebraic geometry than has yet been understood. The workshop brought into contact experts from commutative algebra and algebraic geometry working on these problems – it provided opportunities to get updated on the latest developments through talks of the participants, but also reserved time for working groups in which participants brainstormed ideas and insights in the context of high-intensity discussions aimed at initiating immediate progress on proposed problems, thereby setting the stage for on-going collaborations after the workshop.
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Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Tomasz Szemberg, Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry. Oberwolfach Rep. 13 (2016), no. 1, pp. 653–702