Let X be a Kahler complex manifold and let Z be a complex submanifold. Within the framework of derived deformation theory, the AbelJacobi map for the pair (X,Z) has a natural interpretation as a morphism form a homotopy fiber to a double homotopy fiber. Using this fact and the dictionary between formal moduli problems and differential graded Lie algebras up to homotopy, it is easy to describe a linear Linfinity morphism encoding the AbelJacobi map, and in terms of this Linfinity morphism it is immediate to reobtain the classical description of the differential of the AbelJacobi map as well as the result that Bloch's semiregularity map annihilates the obstructions to deforming Z inside X. This provides a geometrical interpretation of recent results by IaconoManetti and Pridham.
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Abel, Jacobi and the double homotopy fiber
Research Group:
Prof.
Domenico Fiorenza
Institution:
Universita' di Roma "La Sapienza"
Location:
A134
Schedule:
Wednesday, March 5, 2014  09:30 to 11:00
Abstract:
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Carlo Scarpa
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Dan Kucerovsky
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