In this paper we illustrate an algorithmic procedure which allows to build projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T. The main step of the construction, inspired by , is a combinatorial algorithm that produces a toric variety by subdividing in a suitable way a given smooth fan
Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3]. In this paper we describe their integer cohomology rings by generators and relations.
Let M(A) be the complement in C2 of a complexified line arrangement. We provide compact formulas for a Morse complex which computes the (co)homology of M(A) with coefficients in an abelian local system. This refines and simplifies, in the two-dimensional case, a general construction appeared in [M. Salvetti, S. Settepanella, Combinatorial Morse theory and minimality of hyperplane arrangements, Geom. Topol. 11 (2007) 1733–1766], giving also a direct geometrical interpretation
Blowup and chomology bases 317Theorem 1.4. (see [1]) Let G be a building set containing (C n ) * and let Y G be the compact model associated to the linear subspace arrangement induced by G in P(C n ). Then Y G is the total space of a line bundle on D (C n ) * and Y G is isomorphic to D (C n ) * .This means that the projective case is included in the one described above.
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