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arXiv · 2212.07584

Syzygies of tangent developable surfaces and K3 carpets via secant varieties

Jinhyung Park
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Abstract

We give simple geometric proofs of Aprodu-Farkas-Papadima-Raicu-Weyman's theorem on syzygies of tangent developable surfaces of rational normal curves and Raicu-Sam's result on syzygies of K3 carpets. As a consequence, we obtain a quick proof of Green's conjecture for general curves of genus $g$ over an algebraically closed field $\mathbf{k}$ with $\operatorname{char}(\mathbf{k}) = 0$ or $\operatorname{char}(\mathbf{k}) \geq \lfloor (g-1)/2 \rfloor$. We also show the arithmetic normality of tangent developable surfaces of arbitrary smooth projective curves of large degree.

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Jinhyung Park. 2022-12-15. Syzygies of tangent developable surfaces and K3 carpets via secant varieties. https://arxiv.org/abs/2212.07584

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