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Sheaves on fans and posets

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
依托单位国家:
加拿大
项目类别:
Discovery Grants Program - Individual
财政年份:
2009
资助国家:
加拿大
项目状态:
已结题
起止时间:
2009-01-01 至 2010-12-31
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中文摘要
翻译
扇上层的概念起源于代数几何,作为复曲面簇的等变上同调的组合描述。该理论的主要应用是在组合数学中-证明各种组合定义的数的非负性。举两个例子,g向量的非负性(硬莱夫谢茨定理)和cd指标的非负性。本文的目的是研究扇和偏序集上的层理论,并将其应用于组合数学的两个领域--Charney-Davis猜想和Billera和Brenti构造的Bruhat图的非齐次cd-指标。
英文摘要
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.
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Combinatorial problems in the theory of toric varieties
  • 批准号:
    RGPIN-2020-04335
  • 项目类别:
    Discovery Grants Program - Individual
  • 资助金额:
    $1.75万
  • 财政年份:
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  • 负责人:
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  • 依托单位:
Combinatorial problems in the theory of toric varieties
  • 批准号:
    RGPIN-2020-04335
  • 项目类别:
    Discovery Grants Program - Individual
  • 资助金额:
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  • 财政年份:
    2021
  • 负责人:
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  • 依托单位:
Combinatorial problems in the theory of toric varieties
  • 批准号:
    RGPIN-2020-04335
  • 项目类别:
    Discovery Grants Program - Individual
  • 资助金额:
    $1.75万
  • 财政年份:
    2020
  • 负责人:
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  • 依托单位:
Algebraic geometry of toric varieties and its applications to combinatorics.
  • 批准号:
    RGPIN-2015-05787
  • 项目类别:
    Discovery Grants Program - Individual
  • 资助金额:
    $1.02万
  • 财政年份:
    2019
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  • 依托单位:
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