The Prym-canonical Clifford index

We introduce two new invariants of Prym curves, the Prym-canonical Clifford index and the Prym-canonical Clifford dimension. The former is a nonnegative integer (according to Prym-Clifford’s theorem), while the latter is a pair of nonnegative ordered integers. We classify Prym curves with Prym-canonical Clifford index equal to 0,1,2. By specialization to hyperelliptic curves, we compute the Prym-canonical Clifford index of a general Prym curve and show that its Prym-canonical Clifford dimension is (0,0).

💡 Research Summary

The paper introduces two novel invariants attached to a Prym curve ((C,\eta)): the Prym‑canonical Clifford index (\operatorname{Cliff}\eta(C)) and the Prym‑canonical Clifford dimension (\dim\operatorname{Cliff}\eta(C)). Here (\eta) is a non‑trivial 2‑torsion line bundle on a smooth curve (C) of genus (g\ge 2), and the Prym‑canonical linear series is (|\omega_C\otimes\eta|). For any line bundle (L) on (C) satisfying (h^0(L)\ge1) and (h^0(L\otimes\eta)\ge1) the authors define
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