Existence of Crepant resolutions for two-parameter Gorenstein Cyclic Quotient Singularities

TL;DR

This paper establishes a condition for the existence of crepant resolutions in two-parameter Gorenstein cyclic quotient singularities using the remainder polynomial across any dimension.

Contribution

It introduces a new criterion based on the remainder polynomial to determine crepant resolutions for these singularities.

Findings

Derived a necessary and sufficient condition for crepant resolutions

Applicable to cyclic quotient singularities in any dimension

Provides a polynomial-based criterion for algebraic geometers

Abstract

In this paper, we show a condition for two-parameter Gorenstein cyclic quotient singularities to have a crepant resolution by using the remainder polynomial in any dimension.