Under what conditions on a curve $C$, defined over a ring $R$, is its symmetric square, $C^{(2)}$ smooth/proper? Is it enough for $C$ itself to be smooth/proper over $\text{Spec}R$?
How does one see this? Is there any reference to these statements?
2026-05-16 22:18:14.1778969894
Properties of the symmetric square of a curve
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