For n≥15, the moduli space of n-pointed genus-3 curves is of general type, completing the Kodaira classification of pointed genus-3 moduli spaces.
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The Kodaira classification of the moduli space of pointed curves in genus $3$
For n≥15, the moduli space of n-pointed genus-3 curves is of general type, completing the Kodaira classification of pointed genus-3 moduli spaces.