Syzygies of tangent developable surfaces and K3 carpets via secant varieties

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 $\mathrm{char}(\mathbf{k})=0$ or $\mathrm{char}(\mathbf{k})\ge \lfloor (g-1)/2\rfloor$. We also show the arithmetic normality of tangent developable surfaces of arbitrary smooth projective curves of large degree.

16 pages. Comments are welcome

Cited by in corpus (1)

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