Del Pezzo surfaces with infinite automorphism groups

Ivan Cheltsov, Yuri Prokhorov
2021 Algebraic Geometry  
We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups and describe the connected components of their automorphisms groups. Everywhere below, the number n 0 refers to the corresponding surface in Table 3 in Section 8. As a consequence of our classification we have the following. Corollary 1.2. Let X be a Du Val del Pezzo surface. Then the group Aut(X) is not reductive if and only if X is one of the 23 surfaces 7 Del Pezzo surfaces with Du Val
more » ... s Let X be a Du Val del Pezzo surface with d := K 2 X . Then d is known as the degree of the surface X. Let µ : X → X be the minimal resolution of singularities. Then so that X is a weak del Pezzo surface, that is, the anticanonical divisor −K X is nef and big. By the Noether formula, d = 10 − ρ(X) 9, and by the genus formula, every irreducible curve on X with negative self-intersection number is either a (−1)-or a (−2)-curve. Moreover, one of the following holds (see [Bre80, HW81] ):
doi:10.14231/ag-2021-008 fatcat:6g37ul2b4rezfb47v63wbjo6im