11 problems

Let $\mathcal{M}_g^0$ be the open moduli space under consideration, and let $\mathcal{Z}_{g,i}$ be the locus of curves $C$ for which there exists a pencil $A\in W^1_k(C)$ such that…

Fulton–Lazarsfeld's connectivity conjecture. If

Bondal's conjecture. For every $k\in\{0,1,\dots,r-1\}$, $D_{2k}(\pi)$ has an irreducible component of dimension at least $2k+1$.

Göpel's orbital degeneracy-locus conjecture. Let $v$ be a general element of $\Delta$. Then:

Tropical Brill–Noether cycle conjecture. Assume $\rho\geq 0$. Then there exists a canonical tropical subvariety $Z^r_d\subseteq W^r_d$ of pure dimension $\rho$ such that

Let $g\in\mathbb{N}$, and let $X$ be an irreducible closed subvariety of the universal family $\mathfrak{A}_g$ defined over $\overline{\mathbb{Q}}$. Write…

Let $m\geq1$, let $s\in\{m+3,\ldots,2m+3\}$, and set $n=2s-2m-3$. Let $\mathsf{M}_{m,s}$ be the degeneracy locus considered in the paper and let $Z_{n,s,m}$ be the associated varie…

Let $A_1,\dots,A_{m+1}$ be linear operators on ${\mathbb R}^m$, and let ${\mathcal X}$ be their degeneracy locus in ${\mathbb P}^{m-1}({\mathbb R})$. The locus has expected dimensi…

Let $A_1,\dots,A_5$ be real matrices whose degeneracy locus ${\mathcal X}:={\mathcal X}(A_1,\dots,A_5)$ is formed from the associated ten lines in ${\mathbb P}^3$. Desargues config…

Let $\Sigma^\wedge_{\infty,i}$ and $\Sigma^S_{\infty,i}$ denote the stable skew-symmetric and symmetric degeneracy loci, and write their Segre–Schwartz–MacPherson classes as formal…

Let $X$ be a connected Fano variety of dimension $n$ and let $\pi$ be a Poisson structure on it. For an integer $k\geq 0$ satisfying $2k<n$, define the degeneracy locus…