论文标题
切线可开发表面和K3地毯通过割线品种的syzygies
Syzygies of tangent developable surfaces and K3 carpets via secant varieties
论文作者
论文摘要
我们提供了简单的几何证明，证明了关于理性正常曲线的切线可开发表面和raicu-sam对K3地毯的syzygies的相切可开发表面的syzygies定理的简单几何证明。结果，我们可以快速证明格林在代数封闭的字段$ \ mathbf {k} $的一般曲线中的猜想，并带有$ \ permatatorName {char}（\ m athbf {k}）= 0 $或$或$ \ \ \ \ \ \ \ \ \ \ peratatorname {char}（char}（\ char geq） \ rfloor $。我们还显示了大程度的任意光滑射击曲线的切线开发表面的算术正态性。
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.
