Formality of derived intersections

Abstract

We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if $X$ is a complex submanifold of a complex manifold $Y$, we prove that $X$ can be quantized if and only if the derived intersection of $X^2$ and ${\Delta }_Y$ is formal in ${\mathrm{D}}^{\mathrm{b}}\left(X^2\right)$.