# University of Toronto's Symplectic Geometry Seminar

Dec. 02 2002, 2:10pm

SS5017A

## Liat Kessler

###
Hebrew University

##
Holomorphic shadows in the eyes of model
theory

** Abstract: **
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.