# Jarle Stavnes (UiO): Birational rigidity of quartic threefolds

**Abstract:** We will summarize the main outline of the proof of the result by Iskovskih-Manin, which states that any birational map between hypersurfaces of degree 4 in P^4 is an isomorphism. Coupled with the already known examples of unirational quartic threefolds by Segre, this gives a negative answer to the Lüroth problem for quartic threefolds. We will also take a brief look at the weak factorization theorem for birational maps.

Published Oct. 19, 2017 7:16 PM
- Last modified Oct. 19, 2017 7:16 PM