The integer cohomology algebra of toric arrangements
Copyright policy )The integer cohomology algebra of toric arrangements
We compute the cohomology ring of the complement of a toric arrangement with integer coefficients and investigate its dependency from the arrangement's combinatorial data. To this end, we study a morphism of spectral sequences associated to certain combinatorially defined subcomplexes of the toric Salvetti category in the complexified case, and use a technical argument in order to extend the results to full generality. As a byproduct we obtain: -a "combinatorial" version of Brieskorn's lemma in terms of Salvetti complexes of complexified arrangements, -a uniqueness result for realizations of arithmetic matroids with at least one basis of multiplicity 1.
Improved and expanded exposition, 42 pages, 3 figures
- University of Pisa Italy
- University of Fribourg Switzerland
Configurations and arrangements of linear subspaces, Hyperplane arrangements, Cell complexes, Arithmetic matroids, Combinatorial topology, toric arrangements, posets, Posets, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Toric varieties, Newton polyhedra, Okounkov bodies, Small categories without loops, combinatorial topology, Salvetti complex, Orlik-Solomon algebra, Combinatorial aspects of matroids and geometric lattices, cell complexes, Toric arrangements, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Orlik–Solomon algebra, Relations with arrangements of hyperplanes, hyperplane arrangements, info:eu-repo/classification/udc/51, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), General theory of spectral sequences in algebraic topology, small categories without loops, arithmetic matroids
Configurations and arrangements of linear subspaces, Hyperplane arrangements, Cell complexes, Arithmetic matroids, Combinatorial topology, toric arrangements, posets, Posets, FOS: Mathematics, Mathematics - Combinatorics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Toric varieties, Newton polyhedra, Okounkov bodies, Small categories without loops, combinatorial topology, Salvetti complex, Orlik-Solomon algebra, Combinatorial aspects of matroids and geometric lattices, cell complexes, Toric arrangements, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Orlik–Solomon algebra, Relations with arrangements of hyperplanes, hyperplane arrangements, info:eu-repo/classification/udc/51, Combinatorics (math.CO), Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), General theory of spectral sequences in algebraic topology, small categories without loops, arithmetic matroids
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