A note on Griffiths infinitesimal invariant for curves

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Given a generic curve of genus g4 and a smooth point L∈ Wg₋₁¹(C), whose linear system is base-point free, we consider the Abel-Jacobi normal function associated to L⊗ ²⊗ ωC⁻¹, when (C,L) varies in moduli. We prove that its infinitesimal invariant reconstruct the couple (C,L). When g=4, we obtain the generic Torelli theorem proved by Griffiths.