5 problems

Let $V$ be a smooth projective variety, and let $L$ and $M$ be line bundles on $V$. The Gaussian map is … where $\Delta$ is the diagonal in $V\times V$, $L\boxtimes M$ is the exter…

Let $\mathcal{S}_g$ denote the moduli space of smooth genus-$g$ spin curves, and let $\mathcal{S}_g^r$ denote the locus of spin curves whose theta-characteristic has at least $r+1$…

Let $C$ be a cyclic trigonal curve, and let $xi_p^1,\ldots,\xi_p^l$ denote the indicated tangent directions at a point $p$, with $l<2g-2$. An asymptotic direction is a direction an…

Let $C\subset\mathbb{P}^{g-1}$ be a non-hyperelliptic canonical curve of genus $g\geq 8$ with Clifford index greater than $2$, and let $\mathcal{I}_C$ be its ideal sheaf. Wahl's va…

Let $Z=G/P\times G/P$, where $G/P$ is a rational homogeneous variety, and let the diagonal copy of $G/P$ be the subvariety of $Z$. A splitting of $Z$ is a section of $K_Z^{1-p}$ de…