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On projective manifolds with semi-positive holomorphic sectional curvature

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This study aims to establish structure theorems for projective manifolds with semi-positive holomorphic sectional curvature, particularly exploring rational connection and morphisms.
Provided structure theorems for smooth projective varieties with semi-positive holomorphic sectional curvature.
Demonstrated rational connectivity under specific conditions regarding tangent vectors and holomorphic curvature.
Established relationships between the universal cover of the variety and complex Euclidean space.
Proved that if the holomorphic sectional curvature is quasi-positive, the variety is rationally connected.
Showed existence of a locally trivial morphism to an abelian variety with a rationally connected fiber.
The universal cover of X is shown to be biholomorphic to the product of complex Euclidean space with the rationally connected fiber.

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Randomized trial establishes structure theorems for projective varieties, implying connections to Yau's conjecture.

Shin‐ichi Matsumura (2022) studied this question.

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