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| Date: | Fri, September 5, 2014 |
| Time: | 11:15 |
| Place: | Prof. Penkov's Office, Room 111, Research I |
Abstract: This is joint work with Peter Feller (University of Bern). We consider algebraic embeddings of a smooth algebraic variety X into complex affine space ℂm. It is natural to ask whether two algebraic embeddings f, g: X → ℂm are algebraically equivalent, i.e. whether there exists an algebraic automorphism φ of ℂm such that φ ⸰ f = g. Srinivas proved that two algebraic embeddings of X into ℂm are algebraically equivalent, provided that 2 dim X + 2 ≤ m. In this talk we discuss the following one-dimensional improvement under a relaxed equivalence condition.
Theorem.
If f, g: X → ℂm are algebraic embeddings and 2 dim X + 1 ≤ m, then there exists a holomorphic automorphism φ of ℂm such that φ ⸰ f = g.
In fact, the proof is based on an idea of Kaliman, with which he proved
that two algebraic embeddings of ℂ into ℂ3 are holomorphically equivalent. In the course of this talk, we discuss this idea.