Deformations of curves on a higher dimensionalalgebraic variety and their obstructions

点击翻译按钮获取中文摘要

We study the first order infinitesimal deformations of degenerate curves on a uniruled algebraic variety of dimension at least 3 and their obstructions. As a result, we give two different geometric interpretations of infinitesimal deformations with poles (rational sections of the normal bundle of hypersurfaces). By using the liaison theory, we give a classification of the irreducible components of the Hilbert scheme for a certain class of space curves. We also study the deformations of space curves lying on a smooth quartic surface of Picard number 2, and construct a new example of families of curves with obstructed first order infinitesimal deformations.