English

The Hirzebruch genera of complete intersections

Algebraic Topology 2020-05-04 v2 Algebraic Geometry

Abstract

Following Brooks's calculation of the A^\hat{A}-genus of complete intersections, a new and more computable formula about the A^\hat{A}-genus and α\alpha-invariant will be described as polynomials of multi-degree and dimension. We also give an iterated formula of A^\hat{A}-genus and the necessary and sufficient conditions for the vanishing of A^\hat{A}-genus of complex even dimensional spin complete intersections. Finally, we obtain a general formula about the Hirzebruch genus of complete intersections, and calculate some classical Hirzebruch genera as examples.

Keywords

Cite

@article{arxiv.2003.02049,
  title  = {The Hirzebruch genera of complete intersections},
  author = {Jianbo Wang and Zhiwang Yu and Yuyu Wang},
  journal= {arXiv preprint arXiv:2003.02049},
  year   = {2020}
}

Comments

Revised version: Remarks 3.3 and 3.4 are removed due to an error in 3.4. Some arguments simplified. Comments are welcome!

R2 v1 2026-06-23T14:03:37.869Z