Given a generic curve of genus $g\geqslant4$ and a smooth point $L\inW_{g-1}^{1}(C)$, whose linear system is base-point free, we consider theAbel-Jacobi normal function associated to $L^{\otimes 2}\otimes\omega_{C}^{-1}$, when $(C,L)$ varies in moduli. We prove that itsinfinitesimal invariant reconstruct the couple $(C,L)$. When $g=4$, we obtainthe generic Torelli theorem proved by Griffiths.
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机译:给定一般曲线$ g \ geqslant4 $和一个光滑点$ L \ inW_ {g-1} ^ {1}(C)$,其线性系统没有基点,我们考虑关联的Abel-Jacobi法线到$ L ^ {\ otimes 2} \ otimes \ omega_ {C} ^ {-1} $,当$(C,L)$的模数变化时。我们证明了它的无穷小不变性重构了夫妇$(C,L)$。当$ g = 4 $时,我们获得了格里菲斯(Griffiths)证明的通用Torelli定理。
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