Ullemar's formula for the moment map, II

TL;DR

This paper extends Ullemar's formula to complex polynomial domains, demonstrating that the Jacobian of the complex moment map equals the self-resultant of the defining polynomial, thus linking geometric and algebraic properties.

Contribution

It introduces the complex analogue of Ullemar's formula, connecting the Jacobian of the moment map with the self-resultant of the polynomial defining the domain.

Findings

Jacobian of the complex moment map equals the self-resultant of the polynomial

Established the complex analogue of Ullemar's formula

Bridged geometric and algebraic properties of polynomial domains

Abstract

We establish the complex analogue of Ullemar's formula for polynomial domains. We show that the Jacobian of the complex moment mapping is equal to the self-resultant of the defining polynomial.