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arXiv · 2305.19085

Hard Lefschetz theorems for free line bundles

Jiajun Hu·Shijie Shang·Jian Xiao
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Abstract

We introduce a partial positivity notion for algebraic maps via the defect of semismallness. This positivity notion is modeled on $m$-positivity in the analytic setting and $m$-ampleness in the geometric setting. Using this positivity condition for algebraic maps, we establish K\"ahler packages, that is, Hard Lefschetz theorems and Hodge-Riemann bilinear relations, for the complete intersections of Chern classes of free line bundles.

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Jiajun Hu, Shijie Shang, Jian Xiao. 2023-05-30. Hard Lefschetz theorems for free line bundles. https://arxiv.org/abs/2305.19085

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