Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets
Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets
复制标题
高维定点集的双曲定位和 Lefschetz 定点公式
DOI：
10.1093/imrn/rnx030
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Yutaka Matsui and Kiyoshi Takeuchi
中科院分区：
文献类型：
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作者：
Yuichi Ike;Yutaka Matsui and Kiyoshi Takeuchi
我们研究了具有高维不动点集的可构层的Lefschetz不动点公式。在相当弱的假设下，我们证明了它们的局部贡献是由一些与双曲局部化有关的可构造函数表示的。这肯定地回答了Goresky-MacPherson的一个猜想，特别是对于光滑不动点分量(见[，第9页，(1.12)公开问题])。在证明过程中，我们将有效地使用前面文章中介绍的新的拉格朗日循环。此外，我们还给出了用我们的方法可以显式确定局部贡献的各种例子。
We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions associated to hyperbolic localizations. This gives an affirmative answer to a conjecture of Goresky–MacPherson in particular for smooth fixed point components (see [, page 9, (1.12) Open problems]). In the course of the proof, the new Lagrangian cycles introduced in our previous article will be effectively used. Moreover, we show various examples for which local contributions can be explicitly determined by our method.