A note on the Eisenbud-Mazur Conjecture

TL;DR

This paper computationally verifies the Eisenbud-Mazur conjecture for specific prime ideals in formal power series rings, providing evidence for its validity in certain cases within regular local rings.

Contribution

It offers the first computational proof of the conjecture for particular prime ideals in formal power series rings, advancing understanding of the conjecture's scope.

Findings

Conjecture holds for certain prime ideals in formal power series rings

Computational methods can verify the conjecture in specific cases

Supports the conjecture's validity in special algebraic settings

Abstract

The Eisenbud-Mazur conjecture states that given an equicharacteristic zero, regular local ring (R,\mathfrak{m}) and a prime ideal P\subset R, we have that P^{(2)}\subseteq mP. In this paper, we computationally prove that the conjecture holds in the special case of certain prime ideals in formal power series rings.