Tohoku Mathematical Journal
2025
December
SECOND SERIES VOL. 77, NO. 4

Tohoku Math. J.
77 (2025), 445-471

Title CURVATURE OPERATOR OF HOLOMORPHIC VECTOR BUNDLES AND $L^2$-ESTIMATE CONDITION FOR $(N,Q)$ OR $(P,N)$-FORMS

Author Yuta Watanabe

(Received March 14, 2022, revised November 28, 2023)
Abstract. The characterization of Nakano semi-positivity by $L^2$-estimate is already known by Deng-Ning-Wang-Zhou's recent work. Stimulated by this work, we study the positivity properties of the curvature operator for holomorphic Hermitian vector bundles. Applying our results, we give a new characterization of Nakano semi-negativity.

Mathematics Subject Classification. Primary 32L05; Secondary 41A36.
Key words and phrases. $L^2$-estimates, singular Hermitian metrics, Nakano positivity.

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