When C is a smooth projective connected complex curve of genus g>1, the Ceresa cycle associated to C is the cycle C - [-1]_*C in the jacobian J of C. The Ceresa cycle is homologically trivial and hence, by an Abel-Jacobi type construction due to Griffiths, it gives rise to a point in a higher intermediate jacobian associated to J. The Griffiths Abel-Jacobi construction varies well in families and gives rise to a ``normal function'' on the moduli space of curves M_g. This normal function in turn gives rise to an interesting smoothly metrized holomorphic line bundle on M_g, called the Hain-Reed line bundle. We study the degeneration behavior of this metrized line bundle near the boundary of M_g in the Deligne-Mumford compactification, and answer a question of Hain. Following Hain we discuss a relation with slope inequalities for families of curves. Joint work with Farbod Shokrieh.

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