14 problems

Let an F-curve be an irreducible one-dimensional boundary stratum in the moduli space $\overline{\operatorname{M}}_{g,n}$, and let a type 6 F-curve denote an F-curve in the sixth c…

Let $\overline{\operatorname{M}}_{g,n}$ be the moduli space of stable $n$-pointed curves, and let $\overline{\operatorname{NE}}_1(\overline{\operatorname{M}}_{g,n})$ be its cone of…

Let $\overline{\operatorname{M}}_{g,n}$ be the moduli space of stable $n$-pointed curves, and let $F_5^{i,j}(I,\emptyset)$ denote a type 5 F-curve with parameters $i,j$ and marking…

Let $\overline M_{0,n}$ be the moduli space of stable genus-zero curves with $n$ marked points. Let $\operatorname{PBDcone}(n)$ be the cone associated with effective partition bloc…

Let $\overline M_{0,n}$ be the moduli space of stable genus-zero curves with $n$ marked points. A divisor is F-nef if it intersects non-negatively with all one-dimensional boundary…

Let $\overline M_{0,n}$ be the moduli space of stable genus-zero curves with $n$ marked points, with the natural action of the symmetric group $S_n$. A divisor is F-nef if it inter…

Let $\overline M_{0,n}$ be the moduli space of stable genus-zero curves with $n$ marked points. A divisor on $\overline M_{0,n}$ is F-nef if it intersects non-negatively with all o…

Let $\overline M_{g,n}$ be the Deligne–Mumford moduli space of stable curves. A divisor on $\overline M_{g,n}$ is F-nef if it intersects non-negatively with all one-dimensional bou…

Let $\overline{\mathcal{M}}_{g,n}$ be the moduli space of stable curves, and let an F-curve be a one-dimensional codimension-$3g-4+n$ boundary stratum. A line bundle is F-nef if it…

Fix $r>0$. For integers $k$, $n$, and labels $a_1,\ldots,a_n$, consider the difference of conformal-block divisors on $\overline{\mathcal{M}}_{0,n}$ associated with the Virasoro ve…

Base-point-freeness conjecture. For any integral $S_n$-invariant F-nef divisor $D$, $2D$ is $G$-base-point-free; in particular, $2D$ is base-point-free.

The $S_n$-invariant F-conjecture. An $S_n$-invariant divisor on $\overline{\mathrm{M}}_{0,n}$ is nef if and only if it is F-nef.

F-conjecture. A divisor on $\overline{\mathrm{M}}_{0,n}$ is nef if and only if it is F-nef.

Let $S$ be the indexing set used in the source, and let $\mathcal{X}_{n+2,(n-2)}$ be the corresponding space. For a divisor $D$ of the form given in the source, define the intersec…