Remarks on Seshadri constants of vector bundles
Let \(X\) be a smooth complex projective variety and \(P\in X\). Here the author introduces the notion of Seshadri constant \(\varepsilon(E,P)\) of an ample vector bundle \(E\) on \(X\) at \(P\), generalizing the case \(\text{rank} (E)=1\) which produced a huge number of nice results. The generalization is successful because the author proves here a theorem which states that \(\varepsilon (E,P)\geq 1\) for \(P\) outside countably many proper subvarieties of \(X\) under assumptions which are natural, but too technical to be stated here. As an application he gives conditions for the spannedness of \(\omega_X\otimes S^t(E) \otimes \det(E)\).
scientific article; zbMATH DE number 1478803
scientific article