Chow rings of toric varieties defined by atomic lattices

Details Chow rings of toric varieties defined by atomic lattices Chow rings of toric varieties defined by atomic lattices

2003-05-09

arxiv.org/abs/math/0305142v2

Invent. Math. 155 (2004) 515-536.

Mathematics

Algebraic Geometry

23 pages, 7 figures, final revision with minor changes, to appear in Invent. Math

Scientific paper

10.1007/s00222-003-0327-2

We study a graded algebra D=D(L,G) defined by a finite lattice L and a subset G in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De Concini and Procesi. Our main result is a representation of D, for an arbitrary atomic lattice L, as the Chow ring of a smooth toric variety that we construct from L and G. We describe this variety both by its fan and geometrically by a series of blowups and orbit removal. Also we find a Groebner basis of the relation ideal of D and a monomial basis of D over Z.

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