Work

Combinatorially minimal Mori dream surfaces of general type

Year: 2026

Type: article

Abstract: In this paper, we suggest a new approach to study minimal surfaces of general type with p g = 0 p_g=0 via their Cox rings, especially using the notion of combinatorially minimal Mori dream space introduced by Hausen [Mosc. Math. J. 8 (2008), pp. 711–757, 847]. First, we study general properties of combinatorially minimal Mori dream surfaces. Then we discuss how to apply these ideas to the study of minimal surfaces of general type with p g = 0 p_g=0 which are very important but still mysterious objects. In our previous paper [Adv. Math. 347 (2019), pp. 708-738], we provided several examples of Mori dream surfaces of general type with p g = 0 p_g = 0 and computed their effective cones explicitly. In this paper, we study their fibrations, explicit combinatorially minimal models and discuss singularities of the combinatorially minimal models. We also show that many minimal surfaces of general type with p g = 0 p_g=0 arise from the minimal resolutions of combinatorially minimal Mori dream surfaces.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9649

Authors: JongHae Keum, Kyoung-Seog Lee

Institutions: Korea Institute for Advanced Study, Pohang University of Science and Technology

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Research Foundation of Korea

Awards: G1188678689, G5209999269