9 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 $(X,E)$ be a smooth Looijenga pair with affine interior $U=X\setminus E$, let $u:\mathcal T\to X$ be the universal torsor, and set $G=\mathcal T|_U$. Let $V$ be the mirror to…

Let $(X,E)$ be a smooth Looijenga pair with affine interior $U=X\setminus E$, let $u:\mathcal T\to X$ be the universal torsor, and set $G=\mathcal T|_U$. Let $U^{\vee}$ and $V$ den…

Closed formula conjecture. The maximum-contact logarithmic Gromov--Witten invariants of this geometry have the closed-form solution stated in the source. The statement was conjectu…

A Looijenga pair is a rational smooth projective surface $S$ together with an anticanonical singular nodal curve $D_1+\cdots+D_l$. Its logarithmic Gromov--Witten invariants are den…

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…

Let $(X,D)$ be a nef Looijenga pair admitting a deformation to a pair $(X',D')$ with $X'$ toric, $D'_i$ prime toric divisors for $i<l$, and $D'_l$ nef. Let $(Y,L)$ be the correspon…

The higher genus log/open correspondence. One has

The genus zero log/local/open correspondence. The invariants satisfy