基于牛顿多边形的曲线亏格公式

Genus Formula of Curve based on the Newton Polygon

曲线的亏格数是重要的双有理不变量,曲线的分类问题便由亏格数给出解答.文中给出了一种计算不可约曲线的亏格的新公式,通过给出一条不可约曲线所对应的牛顿多边形,可以建立单项式变换,因此利用单项式变换达到对曲线奇点的分解,并得到曲线亏格公式中所需的其他变量,这种算法能够更直观更快速的计算曲线的亏格.

The genus of a curve is an important birational invariants, the solution of curves＇classification is by the genus. The paper demonstrates a new formula for the genus of an irreducible curve, by the Newton polygon of an irreducible curve, we can establish monomial transform, so as to resolve the singularity of a curve, and obtain the other invariants of the genus formula, so we can get the genus of a curve more visual and quickly.