6 problems

Strong Maximal Rank Conjecture. The locus $Q^r_d(C)\subset G^r_d(C)$ consisting of linear series for which $\nu(L,V)$ fails to have maximal rank is a determinantal locus of the exp…

Fix positive integers $g,r,d$ with $r\geq 3$ and $\rho(g,r,d)\geq 0$, and let $C$ be a general curve of genus $g$. For a linear series $\ell=(L,V)\in G^r_d(C)$, let…

The maximal rank conjecture. The map $\mu_m$ is either injective or surjective.

The maximal rank prediction. The determinantal locus $X_5(\nu_2)$ has its expected dimension; in this situation, $X_5(\nu_2)=\varnothing$, and consequently no vector bundle $E$ wit…

The strong maximal rank conjecture. For a general $[C]\in\mathcal{M}_g$, the locus $\mathfrak{Quad}_{g,d}^r(C)$ has the expected determinantal dimension

Let $C$ be a smooth curve of genus $g$, and let $G^r_d(C)$ denote the Brill–Noether variety of linear series $l=(L,V)$ of degree $d$ and dimension $r$. Write … and let … be the mul…