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Robin de Jong: Asymptotic properties of the Ceresa cycle

Time: Wed 2021-11-10 14.00 - 15.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

Participating: Robin de Jong (Universiteit Leiden)

Abstract: 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.