Bisectional curvature of complements of curves in \(\mathbb P^2\) (Q2501413)

In the paper under review, it is proven that if \(E\) is a spanned rank 2 vector bundle such that \(c_1^2(E)>c_2(E)\) and \(\det E\) is ample, over a non-singular compact complex surface, then \(E\) is ample and this result is applied to find a list of (reducible) curves \(C\) in \(\mathbb{P}^2\) such that there exists a complete Finsler metric on \(T^*(\mathbb{P}^2\setminus C)\) with holomorphic bisectional curvature \(\leq c^2\), where \(c\) is a constant.