Non-abelian singularity quotients of dimension 3 and varieties of Calabi-Yau (Q1327096)

Let \(G\) be a finite group acting on a complex analytic variety \(X\). The Euler characteristic in the sense of orbifolds of the quotient \(X/G\) is defined as \[ \chi(X,G)= {1\over | G|}\sum \chi(X^{gh}), \] the summation being taken over all commuting pairs \((g,h)\), and \(X^{gh}\) being the set of common fixed points of \(g\) and \(h\). The authors investigate the question, when the quotient \(X/G\) admits a resolution \(\widetilde{X/G}\) with the trivial canonical class such that \(\chi(X,G)= \chi(\widetilde{X/G})\) for a variety \(X\) of dimension 3.