Elliptic surfaces and ample vector bundles.
Let \(E\) be an ample vector bundle of rank \(n-2 \geq 2\) on a complex projective manifold \(X\) of dimension \(n\) having a global section whose zero locus is a smooth surface \(Z\). In this paper the authors determine the structure of pairs \((X,E)\) as above under the assumption that \(Z\) is a properly elliptic surface. This generalizes known results on threefolds containing an elliptic surface as a smooth ample divisor. Among the applications the authors show a conjecture made in their previous work [Forum Math. 9, No. 1, 1--15 (1997; Zbl 0876.14026)].
scientific article; zbMATH DE number 1818899