对数迹与轨道积
Logarithmic trace and orbifold products
摘要：
本文给出了商Deligne-Mumford栈[X/G]的轨道积的一个纯等变结构，其中G是任意线性代数群（不一定是有限的）.我们构造的关键是等变向量丛的“对数迹”的定义。我们还证明了存在一个Orbifold Chern特征标同态，它导致Orbifold Grothendieck环与Orbifold Chow环中的典型被加数的同构。作为应用，我们得到了[X/G]的Grothendieck环上的结合轨道积（与其惯性积相反）.
英文摘要：
We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our construction is the definition of the "logarithmic trace" of an equivariant vector bundle. We also prove that there is an orbifold Chern character homomorphism which induces an isomorphism of a canonical summand in the orbifold Grothendieck ring with the orbifold Chow ring. As an application we obtain an associative orbifold product on the Grothendieck ring of [X/G] (as opposed to its inerita stack) taken with complex coefficients.
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