Department of

# Mathematics

Seminar Calendar
for events the day of Friday, January 21, 2005.

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Friday, January 21, 2005

4:00 pm in 245 Altgeld Hall,Friday, January 21, 2005

#### Non-rationality and birational rigidity of algebraic varieties

###### Tommaso de Fernex (University of Michigan)

Abstract: In the early 70's, motivated by a problem posed by Luroth, Iskovskikh and Manin introduced the "method of maximal singularities" to prove non-rationality for a particular class of projective threefolds. Subsequently, their technique turned out to be a powerful tool in the study of more general properties of algebraic varieties. In this talk I will overview the history of the problem of rationality, discuss Iskovskikh-Manin's theorem and the method of maximal singularities, and present a result (obtained in collaboration with Ein and Mustata) that in particular implies the non-rationality of certain families of projective hypersurfaces.