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- W3106181326 abstract "We prove a strong vanishing result for finite length Koszul modules, and use it to derive Green’s conjecture for every g-cuspidal rational curve over an algebraically closed field $${{mathbf {k}}}$$ , with $${text {char}}({{mathbf {k}}})=0$$ or $${text {char}}({{mathbf {k}}})ge frac{g+2}{2}$$ . As a consequence, we deduce that the general canonical curve of genus g satisfies Green’s conjecture in this range. Our results are new in positive characteristic, whereas in characteristic zero they provide a different proof for theorems first obtained in two landmark papers by Voisin. Our strategy involves establishing two key results of independent interest: (1) we describe an explicit, characteristic-independent version of Hermite reciprocity for $${{mathfrak {s}}}{{mathfrak {l}}}_2$$ -representations; (2) we completely characterize, in arbitrary characteristics, the (non-)vanishing behavior of the syzygies of the tangential variety to a rational normal curve." @default.
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- W3106181326 date "2019-06-15" @default.
- W3106181326 modified "2023-10-16" @default.
- W3106181326 title "Koszul modules and Green’s conjecture" @default.
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- W3106181326 doi "https://doi.org/10.1007/s00222-019-00894-1" @default.
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