On sections with isolated singularities of twisted bundles and applications to foliations by curves
The authors prove two main results: Let \(M\) be a compact Kähler manifold of an ample line bundle \(L\rightarrow M\), and let \(E\rightarrow M\) be a holomorphic vector bundle of rank \(n=\dim M\geq 2\). There exists an integer \(r_0\) such that \(s'=\varphi(s)\) for some endomorphism of \(E\), if \(s, s'\) are two global sections of \(E\otimes L^{\otimes r} (r\geq r_0)\) such that \(s\) has isolated zeros, and such that the closed subscheme of the zero set of \(s'\) contains that of the zero set of \(s\). The above theorem result is valid for \(r_0=1\) and \(n\geq2\), when \(L\) and \(E\) are the hyperplane and tangent bundles of \(\mathbb P^n\) respectively.
scientific article; zbMATH DE number 2064721