3 problems

Let $(p\in X)$ be a cusp singularity equipped with an antisymplectic involution $\iota$ fixed point free on $X\setminus\{p\}$, and let $D$ be its dual cycle. Let $Y$ be a smooth ra…

Let $(p\in X)$ be a cusp singularity equipped with an antisymplectic involution $\iota$. Let $D$ denote the dual cycle of the cusp. An equivariant smoothing conjecture. Then…

Looijenga's conjecture. The cusp $(X,x)$ is smoothable if and only if the minimal resolution of the dual cusp sits on a rational surface.