Some New Properties of Algebraic Curves and Hypersurfaces in Projective Space
射影空间中代数曲线与超曲面的一些新的性质

A new invariant of algebraic curves, i.e. characteristic number is found, and the new higher degree generalizations of Pascal's theorem in the form of quite different from Chasles theorem and Cayley-Bacharach theorem are obtained. Based on these results, some properties of algebraic curves are investigated, and the relationship between Pascal hypersurfaces of degree $m$ and of degree m-1 is given.