Balancing tautological intersection numbers

We prove the three balancing inequalities conjectured by the authors about 20 years ago: moving one unit from a larger index to a smaller one cannot decrease a mixed tautological intersection number, whether the two distinguished insertions are psi classes, kappa classes, or Hodge Chern classes.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.39462
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

Balancing tautological intersection numbers

Kefeng Liu, Hao Xu
arXiv (Cornell University)
Algebraic Geometry and Number Theory
preprint

Balancing tautological intersection numbers

Kefeng Liu, Hao Xu
preprint en

Abstract

We prove the three balancing inequalities conjectured by the authors about 20 years ago: moving one unit from a larger index to a smaller one cannot decrease a mixed tautological intersection number, whether the two distinguished insertions are psi classes, kappa classes, or Hodge Chern classes.

arXiv (Cornell University)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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Balancing tautological intersection numbers — Kefeng Liu, Hao Xu · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS