Let consider a smooth projective curve $X$ over $\mathbb{C}$. We consider the scheme that classifies effective divisors of degree $d$, which is isomorphic to $X^{d}/S_{d}$ where $S_{d}$ is the symmetric group.

We consider the map which associates to an effective divisor D of degree $d$ the sum of its multiplicities greater than two, $\sum\limits_{x,m_{x}(D)\geq 2}m_{x}(D)$.

Is this function is upper-semicontinuous?