The Hirzebruch genera of complete intersections
Algebraic Topology
2020-05-04 v2 Algebraic Geometry
Abstract
Following Brooks's calculation of the -genus of complete intersections, a new and more computable formula about the -genus and -invariant will be described as polynomials of multi-degree and dimension. We also give an iterated formula of -genus and the necessary and sufficient conditions for the vanishing of -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.
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!