Chow rings of toric varieties defined by atomic lattices

• 成果类型: Article
• 署名作者: Feichtner, EM; Yuzvinsky, S
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oregon
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0327-2
• 发表日期: 2004
• 页码: 515-536
• 关键词: intersection theory

摘要

We study a graded algebra D = D(L, g) over Z 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 [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 g. We describe this variety both by its fan and geometrically by a series of blowups and orbit removal. Also we find a Grobner basis of the relation ideal of D and a monomial basis of D.