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Holomorphic shadows in the eyes of model theoryGeometry/Topology
|Speaker: ||Liat Kessler, Hebrew University (visiting UCD)|
|Location: ||693 Kerr|
|Start time: ||Wed, Feb 5 2003, 4:10PM|
An almost complex manifold is a manifold M with a complex
structure J on the fibers of the tangent bundle TM.
A C^infty mapping is called J-holomorphic if its differential
is complex linear at each point of the source.
For technical reasons, our manifolds and maps are real analytic.
A "holomorphic shadow" is the image of a J-holomorphic mapping
from a compact complex manifold. We explore the geometry of
almost complex manifolds by means of model theory.
In model theory, a "structure" is an infinite set D together with
a collection of subsets of D^n closed under intersections, complements,
projections and their inverses, and containing the diagonals.
A complex manifold and its subvarieties give rise to a structure.
This structure satisfies some "dimension axioms". B. Zilber called
a structure that satisfies these axioms a "Z-structure". We expect that
an almost complex manifold with its holomorphic shadows and diagonals
gives a Z-structure.