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 $1\le p+q\le \dim X$ with $\min \{p,q\}\le 1$.

arXiv comment37 pages, all comments all welcome!