# Configuration Spaces: Geometry, Topology and Representation by Filippo Callegaro, Frederick Cohen, Corrado De Concini, Eva

By Filippo Callegaro, Frederick Cohen, Corrado De Concini, Eva Maria Feichtner, Giovanni Gaiffi, Mario Salvetti

This ebook collects the medical contributions of a gaggle of prime specialists who took half within the INdAM assembly held in Cortona in September 2014. With combinatorial ideas because the relevant subject matter, it makes a speciality of contemporary advancements in configuration areas from numerous views. It additionally discusses their functions in parts starting from illustration concept, toric geometry and geometric staff concept to utilized algebraic topology.

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E ; 2/ ! z1 ; z2 / to z2 , z1 , and z1 z2 1 , respectively. E // D C2 along the same fibrations. A/; as predicted by Theorem 14. X/. Therefore, the Tangent Cone theorem shows, once again, that X is not 1-formal. Acknowledgements I wish to thank Stefan Papadima for several useful conversations regarding this work, and also the referee, for a careful reading of the manuscript. This work was supported in part by National Security Agency grant H98230-13-1-0225. Around the Tangent Cone Theorem 37 References 1.

58(3), 257–269 (2015) 26. C. Dupont, Hypersurface arrangements and a global Brieskorn-Orlik-Solomon theorem. Ann. Inst. Fourier. 65(6), 2507–2545 (2015) 27. M. Eastwood, S. Huggett, Euler characteristics and chromatic polynomials. Eur. J. Comb. 28(6), 1553–1560 (2007) 28. M. Falk, Arrangements and cohomology. Ann. Comb. 1(2), 135–157 (1997) 29. M. Falk, S. Yuzvinsky, Multinets, resonance varieties, and pencils of plane curves. Compos. Math. 143(4), 1069–1088 (2007) 30. M. Feichtner, S. Yuzvinsky, Formality of the complements of subspace arrangements with geometric lattices.

1 Complement and Intersection Lattice A hyperplane arrangement A is a finite collection of codimension 1 linear S subspaces in a complex affine space Cn . A/ D Cn n H2A H, is a connected, smooth, quasi-projective variety. This manifold is a Stein domain, and thus has the homotopy-type of a finite CW-complex of dimension n. A/ is the complement in CPn 1 of the projectivized arrangement. The topological invariants of the complement are intimately tied to the combinatorics of the arrangement. A/, which is the poset of all intersections of A, ordered by reverse inclusion.