Chow rings of toric varieties defined by atomic lattices
Chow rings of toric varieties defined by atomic lattices
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DOI：
10.1007/s00222-003-0327-2
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发表时间：
2004-03-01
影响因子：
3.1
通讯作者：
Yuzvinsky, S
中科院分区：
文献类型：
--
作者：
Feichtner, EM;Yuzvinsky, S
研究了由有限格L和L的子集g定义的环Z上的分次代数D=D(L，g)，即所谓的建筑集.这个代数是De Concini和Procesi[2]中发现的超平面排列紧化的上同调代数的推广。我们的主要结果是D的表示，对于任意原子晶格L，它是我们由L和g构造的光滑环簇的Chow环。我们用它的扇形和一系列的爆破和轨道移位来描述这个环簇。给出了D的关系理想的Grobner基和D的单项式基。
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.