9 problems

Let $S$ be a smooth projective surface and let $L$ be a sufficiently ample line bundle on $S$. The Severi degree $N^{(S,L),delta}$ counts $delta$-nodal curves in $|L|$ through…

For a smooth projective plane, let $N^{d,\delta}$ denote the Severi degree, namely the number of possibly reduced $\delta$-nodal degree-$d$ curves passing through general…

Di Francesco–Itzykson conjecture. For fixed $delta$, the Severi degree $N^{d,delta}$ is equal to the node polynomial $N_delta(d)$ for all sufficiently large $d$.

Fix $\delta\ge1$, and write the refined plane Severi degree as … Let $N_\delta(d;y)$ be the refined node polynomial, with coefficients $p^\delta_i(d)$ defined analogously. Coeffici…

Let $\Delta$ be a convex lattice polygon, let $S=X(\Delta)$ be the associated smooth toric surface, and let $L=L(\Delta)$ be a $\delta$-very ample line bundle. Let…

For a projective surface $S$ and line bundle $L$, let $N^{(S,L),\delta}(y)$ denote the refined Severi degree and let $\widetilde N^{(S,L),\delta}(y)$ denote the refined universal i…

Let $S$ be a smooth projective surface, let $L$ be a line bundle on $S$, and let $n_\delta(L)$ denote the Severi degree counting curves in $|L|$ with $\delta$ nodes. Let $X=K_S$ be…

Let $C_\tau(\delta)$ denote the coefficient vector associated with a type $\tau$ in the computation of the node polynomial $N_\delta(d)$. Leading-coefficient polynomiality conjectu…

Göttsche's conjecture. For $\delta\ge1$,