Details:
Title  Chow rings of toric varieties defined by atomic lattices.  Author(s)  Eva Maria Feichtner, Sergey Yuzvinsky  Type  Article in Journal  Abstract  We study a graded algebra D=D(,) over ℤ defined by a finite lattice ℒ and a subset  in ℒ, a socalled 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.  ISSN  00209910; 14321297/e 
URL 
http://link.springer.com/article/10.1007%2Fs0022200303272 
Language  English  Journal  Invent. Math.  Volume  155  Number  3  Pages  515536  Publisher  Springer, Berlin/Heidelberg  Year  2004  Edition  0  Translation 
No  Refereed 
No 
