Improper intersections in complex analytic geometry

Lagrangian intersections in contact geometry

Jet Spaces in Complex Analytic Geometry: an Exposition

In [7] Pillay described the model-theoretic significance of a result in complex analytic geometry due to Campana [1] and Fujiki [2]. These notes are an exposition of the “jet space” constructions that underly the Campana/Fujiki theorem. In particular, we discuss infinitesimal neighbourhoods as well as the sheaves of principal parts, jets, and differential operators. The material is drawn largel...

Lipschitz Geometry of Complex Surfaces: Analytic Invariants and Equisingularity

We prove that the outer Lipschitz geometry of the germ of a normal complex surface singularity determines a large amount of its analytic structure. In particular, it follows that any analytic family of normal surface singularities with constant Lipschitz geometry is Zariski equisingular. We also prove a strong converse for families of normal complex hypersurface singularities in C3: Zariski equ...

Lagrangian intersections in contact geometry ( First draft )

A contactomorphism is a diffeomorphism ψ : M → M which preserves the contact structure ξ. This means that ψα = eα for some smooth function h : M → . A contact isotopy is a smooth family of contactomorphisms ψs : M → M such that ψ sα = e sα for all s. Any such isotopy with ψ0 = id and h0 = 0 is generated by Hamiltonian functions Hs : M → as follows. Each Hamiltonian function Hs determines a Hami...

Overview of Rigid Analytic Geometry

The idea is simple: we want to develop a theory of analytic manifolds and spaces over fields equipped with an arbitrary complete valuation. Of course, it is a standard fact that such a field must be either R, C, or a field with a nonarchimedean valuation, so what we really mean is that we want to develop a theory of nonarchimedean analytic spaces. Doing this näıvely (i.e., defining manifolds in...