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Positivity of supercritical LYZ pairs

Bowen Liu Tsinghua University Mao Sheng Tsinghua University, BIMSA Shing-Tung Yau Tsinghua University, BIMSA

Algebraic Geometry mathscidoc:2610.45001

37, 2026.10
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 K\"ahler manifolds in bidegrees $1\le p+q\le\dim X$ with $\min\{p,q\}\le1$.
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[ Download ] [ 2026-10-22 21:16:58 uploaded by bowen ] [ 16 downloads ] [ 0 comments ] 
@inproceedings{bowen2026positivity,
  title={Positivity of supercritical LYZ pairs},
  author={Bowen Liu, Mao Sheng, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20261022211658963922790},
  pages={37},
  year={2026},
}
Bowen Liu, Mao Sheng, and Shing-Tung Yau. Positivity of supercritical LYZ pairs. 2026. pp.37. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20261022211658963922790.
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