= Diagonal class of complex projective space
{title2=$[\Delta]=\sum_{j=0}^n[\mathbb{CP}^j]\times[\mathbb{CP}^{n-j}]$}
Give <Complex projective space> its complex <orientation>. In the <homology cross product> basis of $H_{2n}(\mathbb{CP}^n\times\mathbb{CP}^n;\mathbb Z)$, the <diagonal> has the displayed class. If $a,b$ are the two normalized degree-two <hyperplane classes>, its <Poincare dual> is $\sum_{j=0}^na^jb^{n-j}$. Indeed every degree-$2n$ monomial $a^rb^{n-r}$ restricts on the <diagonal> to the top power of the hyperplane class, whose evaluation on the <fundamental class> is one. These evaluations determine all coefficients.
Back to article page
