2 problems

Let $X$ be a smooth Fano variety over $\mathbb C$ with Brauer group $Br(X)$. Let $C$ be a smooth connected genus $g$ curve. A component of $\operatorname{Mor}(C,X,\alpha)$ is under…

Let $C$ be a smooth curve of genus $g$, let $G(r,n)$ be a Grassmannian, and let $X_{\ell}$ be a general hypersurface of degree $\ell$ in $G(r,n)$ with $\ell<n$. Denote by…