Degeneration of the modified diagonal cycle

2014/01/13 by Jaya Nn Iyer, Iyer, Jaya N., Stefan Müller–Stach +1
Mathematics · Physics and Astronomy · #14C25 #14D05 #14D20 #14D21 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1401.2796

openalex publication_date 2014/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we revisit the modified diagonal cycle of Gross and Schoen. We look at degenerations of this cycle, induced by a degeneration of the curve C, and explain how the specialization map with respect to the central fiber produces a higher Chow cycle. When C is non-hyperelliptic of genus three, and degenerates to a nodal curve, the degeneration of the cycle corresponds to an indecomposable higher Chow cycle on a curve of genus two.

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