The Hirzebruch genera of complete intersections

Abstract

Following Brooks's calculation of the $\hat{A}$-genus of complete intersections, a new and more computable formula about the $\hat{A}$-genus and $\alpha$-invariant will be described as polynomials of multi-degree and dimension. We also give an iterated formula of $\hat{A}$-genus and the necessary and sufficient conditions for the vanishing of $\hat{A}$-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.

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

References in corpus (1)

• The alpha invariant of complete intersections