#### DOCUMENTA MATHEMATICA, Vol. 19 (2014), 1003-1016

Julien Grivaux

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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