For a (smooth, complex) curve $X$, I know that effective Cartier divisors of degree n are represented by $\text{Sym}^n\left(X\right)$. Say I have a relative divisor $D : Z \to \text{Sym}^n\left(X\right)$, I know "Cartier divisors supported on $D$" are also supposed to be representable. My guess is it's $\text{Sym}^n\left(\text{Supp}\left(D\right)\right)$ but I'm not sure how to define the support of a relative divisor. Can someone help me with that?
2026-04-13 05:05:15.1776056715
Support of a relative Cartier divisor
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