Resumen de Ample vector bundles with sections vanishing along conic fibrations over curves

Tommaso de Fernex

• Let $\mathcal{E}$ be an ample vector bundle of rank $r\geq 2$ on a complex projective manifold $X$ of dimension $n = r+2$ having a section whose zero locus is a smooth surface $Z$. Pairs $(X, \mathcal{E})$ as above are classified under the assumption that $(Z,L_Z)$ is a conic fibration over a smooth curve for some ample line bundle $L$ on $X$.