In
Besse, Arthur L., Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Bd. 10. Berlin etc.: Springer-Verlag. XII, 510 p. DM 198.00 (1987). ZBL0613.53001.
On page 161 there is a suspicious equality $\chi(\mathbb{C}\mathrm{P}^m)=m$. There is nothing in the errata list on last page of the book. Is there something here that I missed it or it is a typo and it should be $\chi(\mathbb{C}\mathrm{P}^m)=m+1$?
This is a typo. All other formulas on the page that follow are for the unreduced Euler characteristic where $\chi(\Bbb{CP}^m) = m+1$.