Positivity of GIT heights of zero-cycles and hyperplane arrangements

TL;DR

This paper proves Zhang's conjecture that the GIT height function, introduced in 1996 for algebraic cycles, is positive specifically for zero-cycles and hyperplane arrangements, advancing arithmetic intersection theory.

Contribution

The paper establishes the positivity of the GIT height function for zero-cycles and hyperplane arrangements, confirming a key conjecture in arithmetic intersection theory.

Findings

Proved positivity of GIT height for zero-cycles

Confirmed positivity of GIT height for hyperplane arrangements

Advances understanding of arithmetic intersection theory

Abstract

In 1996 as part of the development of arithmetic intersection theory and Arakelov theory, Zhang defined a "GIT height function" for semi-stable algebraic cycles in projective space. In the same work, Zhang conjectured that this height function was positive. We prove this conjecture for zero-cycles and hyperplane arrangements.