ℂ*-actions on rational homogeneous varieties and the associated birational maps

Cycle 35th Oral Defence of the Phd Thesis
20 March 2023
Start time 
2:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar room 1 – Department of Mathematics
Doctoral School in Mathematics
Target audience: 
University community
Online – Registration required
Registration email: 
Contact person: 
Prof. Luis Eduardo Solà Conde

Franceschini Alberto - PhD in Mathematics, University of Trento

Given a birational map among projective varieties, it is known that there exists a variety Z with a one-dimensional torus action such that the birational map is induced from two geometric quotients of Z. We proceed in the opposite direction: given a smooth projective variety X with a one-dimensional torus action, one can define a birational map associated to the action and study the properties of the map via the geometry of X. Rational homogeneous varieties admit natural torus actions, so they are a good class of examples to test the general theory. In the thesis, we obtain and discuss some results about the birational maps associated to some one-dimensional torus actions on rational homogeneous varieties.

Supervisor: Luis Eduardo Solà Conde (University of Trento)