A note on Griffiths infinitesimal invariant for curves |
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Authors: | Emanuele Raviolo |
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Institution: | 1. Dipartimento di Matematica “F. Casorati”, Universitá degli Studi di Pavia, Via Ferrata 1, 27100, Pavia, Italy
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Abstract: | Given a generic curve of genus $g\ge 4$ and a smooth point $L\in W_{g-1}^{1}(C)$ , whose linear system is base-point free, we consider the Abel–Jacobi normal function associated with $L^{\otimes 2}\otimes \omega _{C}^{-1}$ , when $(C,L)$ varies in moduli. We prove that its infinitesimal invariant reconstructs the couple $(C,L)$ . When $g=4$ , we obtain the generic Torelli theorem proved by Griffiths. |
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