A Geometrie Approach to Keller's Jacobian Conjecture.
Foreword, Contents, List of Participants, Program
Surjectivity of Certain Injective Semialgebraic Transformations of IRn.
Holomorphic bijections of algebraic sets
We prove that every holomorphic bijection of a quasi-projective algebraic set onto itself is a biholomorphism. This solves the problem posed in [CR].
Injective endomorphisms of algebraic and analytic sets
We prove that every injective endomorphism of an affine algebraic variety over an algebraically closed field of characteristic zero is an automorphism. We also construct an analytic curve in ℂ⁶ and its holomorphic bijection which is not a biholomorphism.
Algebraic approximation of analytic sets definable in an o-minimal structure
Let K,R be an algebraically closed field (of characteristic zero) and a real closed field respectively with K=R(√(-1)). We show that every K-analytic set definable in an o-minimal expansion of R can be locally approximated by a sequence of K-Nash sets.
On the Weierstrass division.
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