14 problems

Let $X$ be a smooth proper Deligne–Mumford stack with projective coarse moduli space, and let $Y$ be a smooth complete intersection in $X$. Let $I^{tw}$ be a point on the twisted L…

Let $\mu:M\to\mathfrak{g}$ be proper, let $0$ be a regular value of $\mu$, assume that $\mu^{-1}(0)$ is nonempty, and suppose that $\mathrm{G}$ acts freely on $\mu^{-1}(0)$. For…

Let $Y$ be the blow-up of a smooth projective threefold $X$ along a curve $C$ such that $g(C)\geq 1$, or $g(C)=0$ and $-K_X.C\geq 0$. The associativity equations of the quantum pro…

Let $X$ be a smooth projective variety, let $\{\gamma_a\}$ and $\{\gamma^a\}$ be dual bases of $H^*(X,\mathbb Q)$, and let $g$ and $k$ be integers with $k>g$. Two-point vanishing c…

Let $X$ be a smooth projective variety. Given a basis $\{\gamma_a\}$ for $H^*(X,\mathbb Q)$, let $x_i,y_i\in H^*(X)$ and let $k\geq 2g-3+r+s$. Using Gathmann's conventions … and ……

Let $X$ be either the Hirzebruch surface $\mathbb F_2$ or the surface $B'$ obtained by blowing up six points on a conic, and let $E$ be its $(-2)$-curve. Let $D$ be an effective di…

Let $X$ be a projective Calabi–Yau $4$-fold. Write $\operatorname{Hilb}^n(X)$ for the Hilbert scheme of $n$ points on $X$, let $L\to X$ be a line bundle, and distinguish Gromov–Wit…

Local Fano threefold genus-zero correspondence. One has

Let $X$ be a sextic $4$-fold, let $\beta$ be a curve class, and let $\rho\in H^{4}(X,\mathbb{Z})$. Denote by $\mathrm{GW}_{0,\beta}(\gamma)$ the genus-zero Gromov–Witten invariant…

Let $f\in\mathbb Q(d_1,d_2)$ be a rational function defined on $\mathbb Z^+\times\mathbb Z^+$ and suppose … and … for some $k\in\mathbb R^+$. If $n_d$ is a sequence recursively def…

Let $(X,\omega)$ be a compact symplectic manifold and let $g\in\mathbb Z$. For fixed classes $H_1,\ldots,H_k\in H^*(X)$, let…

Let $X$ be a smooth projective Calabi–Yau threefold. For a curve class $\beta\beta$ and the rank-one Donaldson–Thomas series $I_\beta(X)$, let $I_0(X)$ denote the degree-zero serie…

Symplectic rational connectedness conjecture. There is a non-zero Gromov–Witten invariant of this form. This conjecture proposes a symplectic analogue of rational connectedness, an…

Let ${\mathfrak X}$ be a toric Calabi–Yau 3-fold, with a Lagrangian brane $L$ and framing parameters $\mathbf t$. Let $\mathcal W_{g,n}({\mathfrak X},L,\mathbf t;x_1,\dots,x_n)$ de…