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TitleChow rings of toric varieties defined by atomic lattices.
Author(s) Eva Maria Feichtner, Sergey Yuzvinsky
TypeArticle in Journal
AbstractWe study a graded algebra D=D(,) over ℤ defined by a finite lattice ℒ and a subset  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 [2]. 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 . We describe this variety both by its fan and geometrically by a series of blowups and orbit removal. Also we find a Gröbner basis of the relation ideal of D and a monomial basis of D.
ISSN0020-9910; 1432-1297/e
URL http://link.springer.com/article/10.1007%2Fs00222-003-0327-2
JournalInvent. Math.
PublisherSpringer, Berlin/Heidelberg
Translation No
Refereed No