A plethora of inertial products
A plethora of inertial products
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DOI：
10.2140/akt.2016.1.85
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发表时间：
2012-09
期刊：
影响因子：
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通讯作者：
D. Edidin;Tyler Jarvis;T. Kimura
中科院分区：
文献类型：
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作者：
D. Edidin;Tyler Jarvis;T. Kimura
对于光滑的Deligne-Mumford堆栈X，我们描述了K(IX)和A*(IX)上的大量惯性积以及相应的惯性陈氏特征。我们通过发展惯性对理论来做到这一点。每个惯性对确定K(IX)上的一个惯性积和A*(IX)上的一个惯性积，以及它们之间的陈氏特征标环同态。我们证明了存在许多惯性对；实际上，X上的每个向量丛V定义了两个新的惯性对。作为特例，我们恢复了Chen-Run、Abramovich-Graber-Vistoli、Jarvis-Kaufmann-Kimura和Edidin-Jarvis-Kimura的Orbilold积和Gonzalez-Lupercio-Segovia-Uribe-Xicotencatl的虚拟积。我们还介绍了一种全新的乘积，我们称之为局部化奥比霍尔德乘积，它定义在K(IX)的复化上。本文所发展的惯性积在随后的文章中被用来描述惯性K理论中的惯性陈级和幂运算理论。这些结构提供了镜像对称性的新表现形式，符合Hyper-Kaehler解析猜想的精神。
For a smooth Deligne-Mumford stack X we describe a large number of inertial products on K(IX) and A*(IX) and corresponding inertial Chern characters. We do this by developing a theory of inertial pairs. Each inertial pair determines an inertial product on K(IX) and an inertial product on A*(IX) and Chern character ring homomorphisms between them. We show that there are many inertial pairs; indeed, every vector bundle V on X defines two new inertial pairs. We recover, as special cases, the orbifold products of Chen-Run, Abramovich-Graber-Vistoli, Jarvis-Kaufmann-Kimura, and Edidin-Jarvis-Kimura and the virtual product of Gonzalez-Lupercio-Segovia-Uribe-Xicotencatl. We also introduce an entirely new product we call the localized orbifold product, which is defined on the complexification of K(IX). The inertial products developed in this paper are used in a subsequent paper to describe a theory of inertial Chern classes and power operations in inertial K-theory. These constructions provide new manifestations of mirror symmetry, in the spirit of the Hyper-Kaehler Resolution Conjecture.