

Iskovskikh Seminar
April 10, 2014 18:00, Moscow, Steklov Mathematical Institute, room 540






Morphisms between Cremona groups and characterization of rational
varieties
A. Avilov^{} ^{} M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract:
Following the paper of Serge Cantat we will classify homomorphisms from
$PGL_{r+1}(\mathbb C)$ to
the group $Bir(M)$ of birational transformations of a complex projective
variety $M$ of dimension $dim(M)\leq r$. As a byproduct, we show that (1) $Cr(m)$
is isomorphic, as an abstract group, to $Cr(n)$ if and only if $n = m$ and (2) $M$
is rational if and only if $PGL_{dim(M)+1}(\mathbb C)$ embeds as a subgroup of $Bir(M)$.

