Work

Weak del Pezzo surfaces with global vector fields

Year: 2024

Type: article

Abstract: We classify smooth weak del Pezzo surfaces with global vector fields over an arbitrary algebraically closed field k of arbitrary characteristic p 0. We give a complete description of the configuration of .1/and .2/-curves on these surfaces and calculate the identity component of their automorphism schemes.It turns out that there are 53 distinct families of such surfaces if p ¤ 2; 3, while there are 61 such families if p D 3 and 75 such families if p D 2. Each of these families has at most one moduli.As a byproduct of our classification, it follows that weak del Pezzo surfaces with nonreduced automorphism schemes exist over k if and only if p 2 f2; 3g. 14E07, 14J26, 14J50, 14L15

Source: Geometry & Topology

DOI: 10.2140/gt.2024.28.3565

Authors: Gebhard Martin, Claudia Stadlmayr

Institutions: University of Bonn, Technical University of Munich

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: University of Utah, Deutsche Forschungsgemeinschaft, Graduate School, Technische Universität München

Award: G2274286565