Jordan bounds for volume-preserving Cremona groups

We show that the Jordan constant for the volume-preserving plane Cremona group $\mathrm{B}\mathrm{i}\mathrm{r}({\mathbb{P}}^2,\mathrm{\Delta })$ is $12$. We provide a Jordan bound of $144$ for the three-dimensional volume-preserving Cremona group $\mathrm{B}\mathrm{i}\mathrm{r}({\mathbb{P}}^3,\mathrm{\Delta })$. We also provide a weak geometric Jordan bound of $2^{11}\cdot 3^2$ for $\mathrm{B}\mathrm{i}\mathrm{r}({\mathbb{P}}^2)$.