Work

On the Iitaka volumes of log canonical surfaces and threefolds

Year: 2025

Type: article

Abstract: Given positive integers and a subset , let denote the set of Iitaka volumes of ‐dimensional projective log canonical pairs such that the Iitaka–Kodaira dimension and the coefficients of come from . In this paper, we show that, if satisfies the descending chain condition, then so does for . In case and , and are shown to share more topological properties, such as closedness in and local finiteness of accumulation complexity. In higher dimensions, we show that the set of Iitaka volumes for ‐dimensional klt pairs with Iitaka dimension satisfies the DCC, partially confirming a conjecture of Zhan Li. We give a more detailed description of the sets of Iitaka volumes for the following classes of projective log canonical surfaces: (1) smooth properly elliptic surfaces, (2) projective log canonical surfaces with coefficients from or . In particular, the minima as well as the minimal accumulation points are found in these cases.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70132

Authors: Guodu Chen, Jingjun Han, Wenfei Liu

Institutions: Shanghai Jiao Tong University, Fudan University, Xiamen University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Natural Science Foundation of Shanghai, National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G1334355585, G1954115938, G2164231362, G653956408