论文标题
代数$ C_2 $ - EquivariantBézout的定理
An algebraic $C_2$-equivariant Bézout's theorem
论文作者
论文摘要
Bézout的定理，非公平性，可以解释为对复杂的投影空间上的欧拉类捆绑总和的计算，以捆绑包的等级及其程度表示。我们使用早期论文的$ C_2 $ -COMPLEX投影空间的共同体来计算$ C_2 $ equivariant上下文的概括。我们使用带有Burnside环系数的普通$ C_2 $ - 生物学，以及定义Euler类所需的扩展分级，我们根据捆绑包的等效等级和捆绑包的程度及其固定子划分来表达。我们使用常数$ \ mathbb {z} $系数和Borel共同体进行类似的计算，并比较结果。
Bézout's theorem, nonequivariantly, can be interpreted as a calculation of the Euler class of a sum of line bundles over complex projective space, expressing it in terms of the rank of the bundle and its degree. We give here a generalization to the $C_2$-equivariant context, using the calculation of the cohomology of a $C_2$-complex projective space from an earlier paper. We use ordinary $C_2$-cohomology with Burnside ring coefficients and an extended grading necessary to define the Euler class, which we express in terms of the equivariant rank of the bundle and the degrees of the bundle and its fixed subbundles. We do similar calculations using constant $\mathbb{Z}$ coefficients and Borel cohomology and compare the results.
