**SMS scnews item created by James East at Wed 8 Jul 2009 1611**

Type: Seminar

Modified: Wed 8 Jul 2009 1614

Distribution: World

Expiry: 13 Jul 2009

**Calendar1: 13 Jul 2009 1205-1255**

**CalLoc1: Carslaw 375**

Auth: jamese@bari.maths.usyd.edu.au

### Algebra Seminar

# Plato’s Cave: What we still don’t know about linear projections

### David Eisenbud

#### Monday July 13, 12:05--12:55pm, Carslaw 375

##### NOTE UNUSUAL DAY

###### Abstract

The theorem that any finite separable field extension has a primitive element (which can be taken to be a linear combination of a given set of generators) has a geometric version: Any algebraic variety (in characteristic zero) can be mapped onto a hypersurface by a linear projection that is an isomorphism on some open dense subset.

How much is the variety necessarily changed by such a projection? This classical question is well understood in low dimension, and very little understood in high dimension.

I'll explain how the question arises in classical and modern algebraic geometry. Then I'll describe some of what is known, and what one might hope. The new parts of what I describe are from recent work with Roya Beheshti.

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After the seminar we will take the speaker to lunch.

In addition to David's talk, there will also be a seminar on Friday; click here for details.

See the Algebra Seminar web page for information about other seminars in the series.

James East jamese@maths.usyd.edu.au