UNIPOTENT GROUP ACTIONS ON DEL PEZZO CONES

Takashi Kishimoto (1) , Yuri Prokhorov (2) , Mikhail Zaidenberg (3)

1 Department of Mathematics, Faculty of Science, Saitama University
2 SMI | RAS - Steklov Mathematical Institute [Moscow]
3 IF - Institut Fourier

In a previous paper we established that for any del Pezzo surface Y of degree at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear system admits an effective Ga-action. In particular, the group Aut(X) is infinite dimensional. In contrast, we show in this note that for a del Pezzo surface Y of degree at most 2 the generalized cones X as above do not admit any non-trivial action of a unipotent algebraic group.

Mots clés: affine cone; automorphism group; anticanonical divisor; unipotent group; del Pezzo surface

Domaines: Géométrie algébrique [math.AG]

Takashi Kishimoto, Yuri Prokhorov, Mikhail Zaidenberg. UNIPOTENT GROUP ACTIONS ON DEL PEZZO CONES. Algebraic Geometry, 2014, 1 (1 January 2015), pp.46-56. ⟨10.14231/AG-2014-003⟩. ⟨hal-00766761v2⟩