15 problems

Let $\mathcal{Y}$ be a gerbe with dual $\widehat{\mathcal{Y}}$ and associated $\mathbb{C}^*$-gerbe $c$. Let $D\subset \mathcal{B}$ be a smooth irreducible divisor, and define its i…

Let $S\subset Y$ be a nonsingular, $T$-invariant divisor, let $\beta\in H_2(Y,\mathbb Z)$ satisfy $\int_\beta[S]\geq 0$, and let $\eta$ be a partition of $\int_\beta[S]$ weighted b…

Let $X$ be a toric Fano surface. Let $D$ be a toric invariant divisor, and let $D^+$ and $D^-$ be disjoint toric invariant divisors. Consider the suitably defined generating series…

Let $B$ be the plane cubic from the preceding setup, let $m_d$ denote the number of degree-$d$ plane curves satisfying (AL) and meeting $B$ at a specified point of order $3d$, and…

Relative descendent GW/PT correspondence.

The marked relative GW/PT correspondence. For all $\gamma\in H^{\ast}((X,D)^r)$, $Z^{(X,D)}_{\mathsf{PT},\beta}(\lambda\mid\tau_{\alpha_1-1}\cdots\tau_{\alpha_r-1}(\gamma))$ is the…

The relative GW/PT correspondence. $Z^{(X,D)}_{\mathsf{PT},\beta}(\lambda\mid\tau_{\alpha_1-1}(\gamma_1)\cdots\tau_{\alpha_r-1}(\gamma_r))$ is the Fourier expansion of a rational f…

Let $E\subset [?]$ be a smooth cubic curve. Relative Gromov--Witten invariants of $(\mathbb{P}^2,E)$ with maximal contact order are compared with local Gromov--Witten invariants of…

Let $\pi:X\to B$ be an elliptic fibration with section and integral fibers, let $D\subset X$ be a nonsingular divisor restricting to an elliptic fibration $\pi_D:D\to A$ over a non…

Let $D$ be a smooth proper Deligne–Mumford stack with projective coarse moduli space, and let $L$ be a line bundle on $D$. Put … Write $\pi:Y\to D$ for the natural projection, and…

Let $S$ be a Del Pezzo surface, let $E$ be a smooth effective anticanonical divisor, and let $\beta\in\operatorname{H}_{2}(S,\mathbb Z)$ be an effective curve class. Set…

Relative descendent GW/Pairs correspondence. Under the variable change $-q=e^{iu}$,

Relative primary GW/Pairs correspondence. For $\gamma_i\in H^*(X,\mathbb Q)$, after the change of variables $e^{iu}=-q$,

Relative descendent GW/Pairs correspondence.

Relative primary GW/Pairs correspondence.