Generic Green's Conjecture and Generic Geometric Syzygy Conjecture in Positive Characteristic
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909607929053184 |
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| author | Wei, Yi |
| author_facet | Wei, Yi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_12187 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generic Green's Conjecture and Generic Geometric Syzygy Conjecture in Positive Characteristic Wei, Yi Algebraic Geometry Commutative Algebra 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. |
| title | Generic Green's Conjecture and Generic Geometric Syzygy Conjecture in Positive Characteristic |
| topic | Algebraic Geometry Commutative Algebra |
| url | https://arxiv.org/abs/2109.12187 |