Bounding the volumes of singular Fano threefolds

Ching-Jui Lai

Let $(X,\Delta )$ be an $n$-dimensional $\epsilon$-klt log $\QQ$-Fano pair. We give an upper bound for the volume $\mathrm{Vol}(-(K_X+\Delta ))=(-(K_X+\Delta ){)}^n$ when $n=2$ or $n=3$ and $X$ is {$\QQ$-factor…