Seminar Algebra and Geometry: Antoine Pinardin (University of Edinburgh)

G-solid varieties

The G-Fano varieties are the varieties whose anticanonical divisor is ample, and whose invariant part of the Picard group has rank one. In the classification of finite subgroups of Cremona up to conjugation, G-Fano varieties play a fundamental role, analogous to the way finite groups are constructed through successive extensions by simple groups. If a G-Fano variety only admits equivariant birational maps to other G-Fano varieties, it is called G-solid. Roughly speaking, this means that the group G is not induced by actions on lower dimensional Fano varieties.

In this talk, I will present the complete answer I gave to the G-solidity problem for surfaces over the field of complex numbers, and some results achieved for threefolds in an ongoing project with Zhijia Zhang.

Veranstaltung übernehmen als iCal