Positivity and the Kodaira embedding theorem

Tight Closure and the Kodaira Vanishing Theorem

The Friedman Embedding Theorem

In this paper, we will present an explicit construction of Harvey Friedman which to every finitely generated group G associates a 2-generator subgroup KG 6 Sym(N) such that G embeds into KG and such that if G ∼= H, then KG = KH .

Some brief notes on the Kodaira Vanishing Theorem

This is a huge topic, because there is a difference between looking at an abstract variety and local equations versus the equations that define a projective variety. Given an abstract variety X and want to imbed in complex projective space, P, then only the canonical line bundle OP (1) is the important object. Let M be a complex manifold of (complex) dimension n. A divisor is defined as follows...

A subgaussian embedding theorem

We prove a subgaussian extension of a Gaussian result on embedding subsets of a Euclidean space into normed spaces. Using the concentration of a random subgaussian vector around its mean we obtain an isomorphic (rather than almost isometric) result, under an additional cotype assumption on the normed space considered.

Non - Quasiconvexity Embedding Theorem

We show that if G is a non-elementary torsion-free word hyperbolic group then there exists another word hyperbolic group G, such that G is a subgroup of G but G is not quasiconvex in G.