English

Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets

Algebraic Geometry 2015-05-26 v2

Abstract

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. In the course of the proof, the new Lagrangian cycles introduced in our previous paper will be effectively used. Moreover we show various examples for which local contributions can be explicitly determined by our method.

Keywords

Cite

@article{arxiv.1504.04185,
  title  = {Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets},
  author = {Yuichi Ike and Yutaka Matsui and Kiyoshi Takeuchi},
  journal= {arXiv preprint arXiv:1504.04185},
  year   = {2015}
}

Comments

38 pages, revised. arXiv admin note: substantial text overlap with arXiv:0812.4480

R2 v1 2026-06-22T09:17:10.483Z