# symmetric powers of connection

Let $\nabla: \mathcal{E} \to \mathcal{E} \otimes \Omega^1_X(\log D)$ be a locally free sheaf on some variety $X$ (smooth, projective, over a field of characteristic 0) endowed with a connection having regular singularities along a normal crossing divisor $D$.

(1) How do you put a connection on the symmetric power $\mathrm{Sym}^k \mathcal{E}$?

(2) Does it have the same singularities?

(3) If so, how are the residues of $\nabla$ and of the symmetric power related?

-
add comment