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

This ebook collects the clinical 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 important topic, it specializes in fresh advancements in configuration areas from quite a few views. It additionally discusses their functions in parts starting from illustration conception, toric geometry and geometric team idea to utilized algebraic topology.

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Trans. Am. Math. Soc. 364(11), 5765–5790 (2012) 12. C. I. Suciu, On Milnor fibrations of arrangements. J. London Math. Soc. (2) 51(1), 105–119 (1995) 13. C. I. Suciu, Characteristic varieties of arrangements. Math. Proc. Camb. Philos. Soc. 127(1), 33–53 (1999) 14. F. de Bobadilla, On homotopy types of complements of analytic sets and Milnor fibres, in Topology of Algebraic Varieties and Singularities. Contemporary Mathematics, vol. 538 (American Mathematical Society, Providence, 2011), pp. 363–367 15.

Feler, Configuration spaces of tori. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 18(2), 139–151 (2007) 32. Y. Félix, S. -C. Thomas, Rational Homotopy Theory. Graduate Texts in Mathematics, vol. 205 (Springer, New York, 2001) 33. Y. Félix, B. -E. Parent, The combinatorial model for the Sullivan functor on simplicial sets. J. Pure Appl. Algebra 213(2), 231–240 (2009) 34. M. Green, R. Lazarsfeld, Deformation theory, generic vanishing theorems and some conjectures of Enriques, Catanese and Beauville.

W/ is a homogeneous subvariety of Cn , which depends only on the analytic germ of W at the identity. W/ ¤ ; if and only if 1 2 W. Moreover, TC1 commutes with finite unions. W/ D fz 2 Cn j exp. z/ 2 W; for all 2 Cg: (27) As shown in [24, 66], this set is a finite union of rationally defined linear subspaces of the affine space Cn . An alternative interpretation of this construction is given in [69, Sect. 3]. It is readily seen that 1 commutes with finite unions and arbitrary intersections. C /n .