Talk by D. Fiorenza

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINARS
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Prof. Domenico Fiorenza (Universita' di Roma "La Sapienza") will 
give a talk on

Abel, Jacobi and the double homotopy fiber

on Wednesday, March 5th, at 9:30 am in Room 134, SISSA building A.

Abstract:

Let X be a Kahler complex manifold and let Z be a complex submanifold.
Within the framework of derived deformation theory, the Abel-Jacobi 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 L-infinity morphism encoding the
Abel-Jacobi map, and in terms of this L-infinity morphism it is immediate
to reobtain the classical description of the differential of the
Abel-Jacobi 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 Iacono-Manetti and Pridham.