6 problems

Fix a rational homology sphere link and consider the general' $\mathbb{Q}$-Gorenstein singularity with that link. Suppose that its fundamental cycle has arithmetic genus at least…

Let $(X,o)$ be a ${\mathbb Q}$-Gorenstein normal surface singularity with ${\mathbb Q}$-homology sphere link, and let $\Delta$ be the splice diagram associated to its resolution gr…

Let $(X,o)$ be a normal ${\mathbb Q}$-Gorenstein surface singularity whose link is a ${\mathbb Q}$-homology sphere. Its universal abelian cover is the finite abelian cover obtained…

Let $(X,o)$ be a ${\mathbb Q}$-Gorenstein normal surface singularity, meaning that its dualizing sheaf has finite order, and suppose that its link is a rational homology sphere. De…

Let $g \geq 18$, and let $m$ be the least common multiple of the exponents of all of the Galois groups of abelian covers of $\mathbf{P}^1$ branched at three points of genus $g$. Un…

Torsion conjecture (T1.5). There exists a finite cover $X$ of $T_\psi$ and a universal tower of finite abelian covers $\{X_i\}$ of $X$ which have exponential torsion homology growt…