## Tokyo Journal of Mathematics

### On an Arithmetical Property of the Normalization of Regular Systems of Weights

Yoshika UEDA

#### Abstract

The weights of a two-dimensional weighted homogeneous polynomial $f$ of degree $h$ corresponding to an isolated singularity are arithmetically characterized by Prof. K. Saito and are called a regular system of weights. Let $m_0$ be the dimension of the vector space of the elements of degree $h$ of the Jacobi ring of $f$. It is shown that $m_0$ is determined by weights and is estimated from below by using the genus of the central curve and the number of branches of a minimal good resolution of the corresponding singularity.

#### Article information

Source
Tokyo J. Math., Volume 15, Number 1 (1992), 1-15.

Dates
First available in Project Euclid: 1 April 2010

https://projecteuclid.org/euclid.tjm/1270130248

Digital Object Identifier
doi:10.3836/tjm/1270130248

Mathematical Reviews number (MathSciNet)
MR1164183

Zentralblatt MATH identifier
0774.14003

#### Citation

UEDA, Yoshika. On an Arithmetical Property of the Normalization of Regular Systems of Weights. Tokyo J. Math. 15 (1992), no. 1, 1--15. doi:10.3836/tjm/1270130248. https://projecteuclid.org/euclid.tjm/1270130248