A combinatorial analog of GKZ theory is constructed for realizable matroids, defining the principal matroid determinant via resultants and introducing a holonomic matroid hypergeometric system whose singular locus is conjectured to coincide with it.
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2026 2verdicts
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A combinatorial sufficient condition for nonresonance of complex rank-one local systems on hyperplane arrangement complements is obtained by refining the Cohen-Dimca-Orlik method, strengthening an earlier theorem and proving a result for line arrangements via restriction and lifting.
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Principal Matroid Determinants
A combinatorial analog of GKZ theory is constructed for realizable matroids, defining the principal matroid determinant via resultants and introducing a holonomic matroid hypergeometric system whose singular locus is conjectured to coincide with it.
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Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements
A combinatorial sufficient condition for nonresonance of complex rank-one local systems on hyperplane arrangement complements is obtained by refining the Cohen-Dimca-Orlik method, strengthening an earlier theorem and proving a result for line arrangements via restriction and lifting.