##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## David Eisenbud

#### MSRI

## The smallest algebraic varieties

##### Abstract:

Any algebraic curve in projective $3$-space that is not contained in a plane has degree at least $3$ -- that is, it meets any plane in at least 3 points. Moreover, any curve of degree $3$, can be parametrised (in suitable coordinates) by \vskip .1in $t--> (t, t^2, t^3)$ \vskip .1in \noindent This was known 150 years ago, and since that time many mathematicians have used and generalized the result. I will describe some of the ideas involved, including recent work of mine with Mark Green, Klaus Hulek and Sorin Popescu.

Host: J. Buhler (CCR)

### September 29, 2005

### 4:00 PM

### AP&M 7321

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