PreprintCC BY 4.0arXiv
Correlation inequalities for volume polynomials
Abstract
We establish sharp correlation inequalities for volume polynomials associated with covers of multisets. These inequalities simultaneously generalize the Khovanskii--Teissier and reverse Khovanskii--Teissier inequalities for intersections of nef divisor classes on projective varieties. They also hold for volume polynomials arising from convex bodies and Hermitian matrices, recovering and extending classical results such as the Alexandrov--Fenchel inequality for mixed volumes of convex bodies and the Hadamard--Fischer inequality for determinants of positive semidefinite matrices. As a combinatorial application, we prove a negative correlation inequality for partitions of bases of matroids that are linearly realizable over a field.
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BibTeX
@misc{huh2026correlation,
title = {{Correlation inequalities for volume polynomials}},
author = {June Huh and Mateusz Michałek and Botong Wang and Jian Xiao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34562},
eprint = {2610.34562},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34562},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Correlation inequalities for volume polynomials
AU - June Huh
AU - Mateusz Michałek
AU - Botong Wang
AU - Jian Xiao
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34562
UR - https://arxiv.org/abs/2610.34562
AB - We establish sharp correlation inequalities for volume polynomials associated with covers of multisets. These inequalities simultaneously generalize the Khovanskii--Teissier and reverse Khovanskii--Teissier inequalities for intersections of nef divisor classes on projective varieties. They also hold for volume polynomials arising from convex bodies and Hermitian matrices, recovering and extending classical results such as the Alexandrov--Fenchel inequality for mixed volumes of convex bodies and the Hadamard--Fischer inequality for determinants of positive semidefinite matrices. As a combinatorial application, we prove a negative correlation inequality for partitions of bases of matroids that are linearly realizable over a field.
ER -