Problem 24.9.1D81AB6932636

Problem 24.9.1.D81AB6932636 Let $u$ and $Y$ be as above, and suppose that $Y$ fails at least one of the two mass properties used in corollary 13.21.5: bounded mass, and the existence of a Hermitian form of positive lower mass. Can the Hermitian background $\Omega $ on $Y$ in theorem 20.3.35 be chosen so that

for every prime divisor $E$ on every smooth modification $\pi $ of $Y$? If so, determine an ordinary or ideal singularity class of this realization that is compatible with changes of background, and prove its addition and approximation properties.