The Hirzebruch quadratic form of a hyperplane arrangement and flat logarithmic connections
classification
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math.AGmath.RT
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arrangementconnectionsflatformhirzebruchhyperplanelogarithmicquadratic
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We prove that the Hirzebruch quadratic form of a complex hyperplane arrangement is non-positive on the set of stable weights, and we identify the zero locus within this set with flat logarithmic connections of a distinguished type. The proof uses Kempf--Ness and the frame-potential inequality.
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