##### Department of Mathematics,

University of California San Diego

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### Analysis Seminar

## Ming Xiao

#### Rutgers University/UIUC

## Nonembeddability into a Fixed Sphere for a Family of Compact Real Algebraic Hypersurfaces.

##### Abstract:

We study the holomorphic embedding problem from a compact real algebraic hypersurface into a sphere. By our theorem, for any integer $N$, there is a family of compact real algebraic strongly pseudoconvex hypersurfaces in $C^2$ , none of which can be locally holomorphically embedded into the unit sphere in $C^N$. This shows that the Whitney (or Remmert) type embedding theorem in differential topology(or in the Stein space theory, respectively) does not hold in the setting above. This is a joint work with Xiaojun Huang and Xiaoshan Li.

### May 1, 2015

### 2:00 PM

### AP&M 7321

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