论文标题
均值同种学环的学位公式
A Degree Formula for Equivariant Cohomology Rings
论文作者
论文摘要
本文概括了lynn的结果。分级模块的程度是其Poincaré系列的一定系数，并且与多重性密切相关。在本文中，我们研究了这些对等模剂共同体学环的交换代数不变。主要定理是度量的添加性公式：$$ deg（h^*_ g（x））= \ sum _ {[a，c] \ in \ Mathcal {q'} _ {max} _ {max}（g，x，x，x）} \ frac {1} {1} {1} {| w_g（a，c） °（h^*_ {c_g（a，c）}（c））。$$我们还展示了该公式如何与交换代数的添加性公式相关联，展示了该度不变的代数和几何特征。
This paper generalizes a result of Lynn on the "degree" of an equivariant cohomology ring $H^*_G(X)$. The degree of a graded module is a certain coefficient of its Poincaré series, and is closely related to multiplicity. In the present paper, we study these commutative algebraic invariants for equivariant cohomology rings. The main theorem is an additivity formula for degree: $$deg(H^*_G(X)) = \sum_{[A,c] \in \mathcal{Q'}_{max}(G,X)}\frac{1}{|W_G(A,c)|} °(H^*_{C_G(A,c)}(c)).$$ We also show how this formula relates to the additivity formula from commutative algebra, demonstrating both the algebraic and geometric character of the degree invariant.
