General curves on elliptic K3 surfaces, and on Halphen surfaces, are the first known smooth k-gonal curves that satisfy the Hurwitz-Brill-Noether dimension theorem.
Explicit B rill- N oether- P etri general curves
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Hurwitz-Brill-Noether theory via K3 surfaces and stability conditions
General curves on elliptic K3 surfaces, and on Halphen surfaces, are the first known smooth k-gonal curves that satisfy the Hurwitz-Brill-Noether dimension theorem.