扭三次曲线的代数性质

Algebraic Properties of Twisted Cubic Curve

扭三次曲线是一条特殊且重要的代数曲线,它是一个一维的代数簇.扭三次曲线在代数几何中常被作为例子来研究各种相关主题比如参数表示,理想,簇的维数等.本文通过研究此曲线的参数表示、维数、切平面以及与理想的关系等代数性质,使我们对扭三次曲线有一个更全面,系统和清晰的认识.

Twisted cubic curve is a special and important algebraic curve, it is one dimensional alge-braic variety. Twisted cubic curve is often regarded as an example to study the properties of related sub-jects such as affine variety, parametric representation, ideal and the dimension of a variety and so on. This article studies the parametric representation of the curve, dimension, tangent plane, the relation-ship between the ideal and the variety so that we have a more comprehensive , system and clear under-standing of twisted cubic curve.