Singularity categories of skewed-gentle algebras

Let $K$ be an algebraically closed field. Let $(Q,Sp,I)$ be a skewed-gentle triple, $(Q^{sg},I^{sg})$ and $(Q^g,I^{g})$ be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra $KQ^{sg}/$ is singularity equivalent to $KQ/$. Moreover, we use $(Q,Sp,I)$ to describe the singularity category of $KQ^g/$. As a corollary, we get that $\mathrm{gldim} KQ^{sg}/<\infty$ if and only if $\mathrm{gldim} KQ/<\infty$ if and only if $\mathrm{gldim} KQ^{g}/< I^{g}><\infty$.Comment: 13 pages, 1 figur