Formality of Derived Intersections

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 $\mathrm{D}^{\mathrm{b}}\bigl (X^2 \bigr)$.

2010 Mathematics Subject Classification: 14C17; 14F05

Keywords and Phrases: intersection theory, derived categories, quantized analytic cycles

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