6 problems

Let $(p\in X)$ be a cusp singularity. A Looijenga pair is a pair $(Y,D)$ consisting of a smooth rational surface $Y$ and an anticanonical divisor $D$ that is a cycle of rational cu…

Let $(p\in X)$ be a cusp singularity, and let its smoothing components be the irreducible components of its smoothing space. Let $(Y,D)$ range over Looijenga pairs corresponding to…

Behnke's conjecture. Every reflexive module on a cusp singularity admits a flat connection.

Let $n$ denote the length of the cycle associated with a symmetric cusp singularity equipped with an antisymplectic involution. Length-12 conjecture. The value $n=12$ is large enou…

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…