On automorphisms and endomorphisms of projective varieties

Michel Brion (1)

1 IF - Institut Fourier

We first show that any connected algebraic group over a perfect field is the neutral component of the automorphism group scheme of some normal projective variety. Then we show that very few connected algebraic semigroups can be realized as endomorphisms of some projective variety X, by describing the structure of all connected subsemigroup schemes of End(X).

Domaines: Géométrie algébrique [math.AG]

Michel Brion. On automorphisms and endomorphisms of projective varieties. Groups of automorphisms in birational and affine geometry, Oct 2012, Levico Terme, Italy. pp.59-81, ⟨10.1007/978-3-319-05681-4_4⟩. ⟨hal-01622799⟩