A characterization of bielliptic curves via syzygy schemes. (English) Zbl 1419.14047
Let \(C\subset \mathbb {P}^{g-1}\) the canonical model of a smooth genus \(g\) curves. If \(g\ge 11\) the authors shows that the second syzygy scheme of \(C\) is \(\ne C\) if and only if \(C\) is a bielliptic curve. For lower \(g\) they classify the second syzygy scheme of the \(4\)-gonal curves. For the proof they first exclude the curves with Clifford index \(\ge 3\) and then analize the \(4\)-gonal curves.
Reviewer: Edoardo Ballico (Povo)
MSC:
| 14H51 | Special divisors on curves (gonality, Brill-Noether theory) |
| 13D02 | Syzygies, resolutions, complexes and commutative rings |
Keywords:
curves; syzygy; bielliptic curve; gonality; second syzygy scheme; tetragonal curve; Clifford indexReferences:
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