##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium

## David Stapleton

#### UCSD

## Measures of Irrationality of Algebraic Varieties

##### Abstract:

A variety is called rational if it is birational to projective space. For example, the only compact, smooth, and rational Riemann surface is the Riemann sphere. A general compact Riemann surface carries two natural invariants which measure its complexity & non-rationality from both a topological and an algebraic perspective: the genus and the gonality. Both of these invariants have classically played a very important role in the study of curves. In higher dimensions there are a number generalizations of these birational invariants which measure the irrationality of an algebraic variety. I will discuss the computation of one of these invariants â€” the degree of irrationality â€” and I will pose a number of open problem about these measures of irrationality.

### October 25, 2017

### 4:00 PM

### AP&M 7218

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