Formality of derived intersections
Julien Grivaux
TL;DR
This paper investigates the conditions under which derived intersections of smooth analytic cycles are formal, focusing on complex submanifolds and their quantization related to derived intersection formality.
Contribution
It establishes necessary and sufficient conditions for the formality of derived intersections in complex analytic geometry, linking quantization to intersection formality.
Findings
Derived intersection of XxX and Δ_Y is formal iff X can be quantized.
Provides criteria for the formality of derived intersections in complex geometry.
Connects formality with quantization conditions for complex submanifolds.
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 XxX and \Delta_Y is formal in D(XxX).
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Algebraic Geometry and Number Theory