Open problems on structure of positively curved projective varieties

TL;DR

This paper discusses open problems and supplements related to the structure of positively curved projective varieties, focusing on fibrations, curvature conditions, and tangent bundle properties.

Contribution

It introduces open problems and supplements to existing structure theorems for certain positively curved projective varieties with specific geometric properties.

Findings

Identification of open problems in the structure theory

Extensions of structure theorems for specific curvature conditions

Insights into the geometry of varieties with nef anti-canonical divisor

Abstract

We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic sectional curvature, pseudo-effective tangent bundle, and nef anti-canonical divisor.