From H\"ormander's $L^2$-estimates to partial positivity

Takahiro Inayama

From H\"ormander's $L^2$-estimates to partial positivity

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arxiv 2008.08287 v3 pith:3AP52CHF submitted 2020-08-19 math.CV math.DG

Takahiro Inayama This is my paper · ORCID

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abstract

In this article, using a twisted version of H\"ormander's $L^2$-estimate, we give new characterizations of notions of partial positivity, which are uniform $q$-positivity and RC-positivity. We also discuss the definition of uniform $q$-positivity for singular Hermitian metrics.

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Siu's curvature positivity and $L^2$ extension theorems for $(p,q)$-forms
math.CV 2026-07 conditional novelty 6.0 of 10

Siu's curvature operator A^E_{p,q} is characterized by an optimal L2 estimate and yields an Ohsawa–Takegoshi extension theorem for (p,q)-forms and local freeness of higher direct images.

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