Hilbert curves of 3-dimensional scrolls over surfaces

摘要

Abstract Let ( X , L ) be a 3-dimensional scroll over a smooth surface Y. Its Hilbert curve is an affine plane cubic consisting of a given line and a conic. This conic turns out to be the Hilbert curve of the Q -polarized surface ( Y , 1 2 det ? E ) , where E is the rank-2 vector bundle ob