Plumbings of lens spaces and crepant resolutions of compound $A_n$ singularities

Bilun Xie, Yin Li

For many compound $A_n$ ($c{A}_n$) singularities $R_f=\mathbb{C}[u,v,x,y]/(uv-f(x,y))$ with crepant resolutions $Y_f$, their mirrors are affine $A_n$ plumbings $W_f^{\circ }$ of $3$-dim…