2 problems

Let $\mathcal{X}=(\mathfrak{X},D,L)$ be a polarized log Fano variety, with integral-point scheme $\mathfrak{U}=\mathfrak{X}\setminus\overline{D}$, height function $H_L$, and counti…

Let $j:X\to J$ be the Iitaka fibration of $X$, and let $\omega_{SF}=\omega_0+dd^c\rho$ be the semi-flat current whose restriction to a generic fiber is the unique fiberwise Ricci-f…