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Positivity of supercritical LYZ pairs
Abstract
We introduce the roots of supercritical Leung--Yau--Zaslow pairs and prove pointwise strong positivity of the associated Schur forms. The resulting LYZ cones contain the pliant cone on smooth projective threefolds, with strict inclusion on a Fujino--Sato threefold. We also establish Hard Lefschetz and Hodge--Riemann relations for the associated Chern classes on compact Kähler manifolds in bidegrees 1≤ p+q≤dim X with min{p,q}≤1.
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BibTeX
@misc{liu2026positivity,
title = {{Positivity of supercritical LYZ pairs}},
author = {Bowen Liu and Mao Sheng and Shing-Tung Yau},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31233},
eprint = {2610.31233},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31233},
}
RIS
TY - UNPB
TI - Positivity of supercritical LYZ pairs
AU - Bowen Liu
AU - Mao Sheng
AU - Shing-Tung Yau
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31233
UR - https://arxiv.org/abs/2610.31233
AB - We introduce the roots of supercritical Leung--Yau--Zaslow pairs and prove pointwise strong positivity of the associated Schur forms. The resulting LYZ cones contain the pliant cone on smooth projective threefolds, with strict inclusion on a Fujino--Sato threefold. We also establish Hard Lefschetz and Hodge--Riemann relations for the associated Chern classes on compact Kähler manifolds in bidegrees 1≤ p+q≤dim X with min{p,q}≤1.
ER -