AAG: A new approach to the extendability of projective varieties: No Gaussian maps

Abstract: The topic of extendability of a projective variety has attracted a lot of attention among algebraic geometers. The approaches to tackle the extendability questions have almost always involved the Gaussian maps of the curve sections. In this talk we introduce a new approach that totally avoids the Gaussian maps of the curve section and a host of issues related to them. As a byproduct of the more general theoretical framework we have developed, we will recover optimal results on extendibility of K3 surfaces with applications to a new proof of the classification of Fano threefolds due to Iskovskih and more generally Mukai varieties. Moreover, we will also discuss new results on the extendability of Calabi-Yau threefolds, where not much is known.These results show interesting parallels and compelling contrasts with the results for its lower dimensional avatar, namely the K3 surface. This work was completed jointly with Jayan Mukherjee.

Host: Matt Kerr