On linear stability and syzygy stability for rank 2 linear series

Abel Castorena; Ernesto C. Mistretta; Hugo Torres

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arXiv · 2001.03609

On linear stability and syzygy stability for rank 2 linear series

Abel Castorena·Ernesto C. Mistretta·Hugo Torres

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Abstract

In previous works, the authors investigated the relationships between linear stability of a generated linear series $|V|$ on a curve $C$, and slope stabillity of the vector bundle $M_{V,L} := \ker (V \otimes \mathcal{O}_C \to L)$. In particular, the second named author and L. Stoppino conjecture that, for a complete linear system $|L|$, linear (semi)stability is equivalent to slope (semi)stability of $M_V$, and the first and third named authors proved that this conjecture holds for hyperelliptic and for generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree $7$.

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BibTeX RIS

Abel Castorena, Ernesto C. Mistretta, Hugo Torres. 2020-01-10. On linear stability and syzygy stability for rank 2 linear series. https://arxiv.org/abs/2001.03609

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