Deformations of curves on a higher dimensionalalgebraic variety and their obstructions

研究了维数至少为3的无界代数簇上退化曲线的一阶无穷小变形及其障碍。因此，我们对极点(超曲面法向丛的有理截面)的无穷小变形给出了两种不同的几何解释。利用联络理论，对一类空间曲线的Hilbert格式的不可约分量进行了分类。我们还研究了位于Picard数为2的光滑四次曲面上的空间曲线的变形，并构造了一个新的一阶受阻小变形曲线族。

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.