Evento

Group Theoretical Characterizations of Rationality

Group Theoretical Characterizations of Rationality
Seminario di Geometria Algebrica del Prof. Andriy Regeta (Università di Padova)

Giovedi 9 ottobre, alle ore 14:30,
Aula B3 a Palazzo Manfredini

Ptof. Andriy Regeta (Università di Padova)

Abstract:  I will discuss the following result, based on a joint work with Cantat, Kraft and van Santen: Let G be 
a solvable group of automorphisms of an affine variety. If G is generated by an irreducible family of automorphisms 
containing the identity, then G is an algebraic group. As an application, I present the following statement: 
a closed connected solvable subgroup of the group of automorphisms Aut(X) of an algebraic variety X has derived 
length less than or equal to dim X +1 and the equality holds iff X is is isomorphic to the affine space A^n. Moreover, 
all Borel subgroups (maximal connected solvable subgroups) of Aut(A^n) of derived length n+1 are conjugate and 
there are many non-conjugate Borel subgroups of Aut(A^n).
I will also discuss the difference between Borel subgroups in Aut(A^n) and in the group of birational transformations of A^n.