Sheaves on fans and posets

风扇和偏心轮上的滑轮

• 批准号: 283301-2009
• 负责人: Karu, Kalle
• 金额: $ 1.89万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=525663
• 关键词: Sheaves; fans; posets

The notion of sheaves on fans originates in algebraic geometry as a combinatorial description of equivariant cohomology of toric varieties. The main application of the theory is in combinatorics -- prooving non-negativity of various combinatorially defined numbers. To mention a couple, non-negativity of the g-vector (the Hard Lefschetz theorem) and non-negativity of the cd-index. This proposal is to study the theory of sheaves on fans and posets with applications in two areas of combinatorics -- the Charney-Davis conjecture and the non-homogeneous cd-index of Bruhat graphs constructed by Billera and Brenti.

扇形上的轴的概念起源于代数几何，是对环面变体的等变上同调的组合描述。该理论的主要应用是在组合学中——证明各种组合定义数的非负性。举两个例子，g向量的非负性（Hard Lefschetz定理）和cd指标的非负性。本文拟研究扇形和偏序集上的束理论及其在两个组合学领域中的应用——Charney-Davis猜想和Billera和Brenti构造的Bruhat图的非齐次cd-索引。