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arXiv · 2109.12187

Generic Green's Conjecture and Generic Geometric Syzygy Conjecture in Positive Characteristic

Yi Wei
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Abstract

We study the syzygies of canonical curves of genus $g\geq 3$ over an algebraically closed field $\mathbb{F}$ of characteristic $p>0$. We provide a new proof of generic Green's Conjecture for $p\geq\frac{g+4}{2}$. Using the techniques from the even-genus case, we establish a significant case of the Geometric Syzygy Conjecture for the last syzygy space of a general even-genus canonical curve (assuming $p>g$). In characteristic 0, it was shown in prior work that this case implies the full conjecture.

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Yi Wei. 2021-09-24. Generic Green's Conjecture and Generic Geometric Syzygy Conjecture in Positive Characteristic. https://arxiv.org/abs/2109.12187

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