Siegel modular forms arising from higher Chow cycles

2025/05/07 by Shouhei Ma, Ma, Shouhei
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2505.04465

Abstract

We prove that the infinitesimal invariant of a higher Chow cycle of type (2,3-g) on a generic abelian variety of dimension g<4 gives rise to a meromorphic Siegel modular form of (virtual) weight Sym⁴det^-1 with bounded singularity, and that this construction is functorial with respect to rank 1 degeneration, namely the K-theory elevator for the cycle corresponds to the Siegel operator for the modular form.

Citations

• The Rank of the Normal Functions of the Ceresa and Gross--Schoen Cycles
• Concomitants of Ternary Quartics and Vector-valued Siegel and Teichmüller Modular Forms of Genus Three
• Specialization of cycles and the K-theory elevator
• The Abel-Jacobi map for higher Chow groups
• The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles
• Constructing Indecomposable Motivic Cohomology Classes on Algebraic Surfaces

Related

• The weight reduction of mod p Siegel modular forms for GSp₄
• Universal abelian variety and Siegel modular forms
• Differentiating Siegel modular forms, and the moving slope of \mathcal A_g
• The geometry of Siegel modular varieties
• Siegel modular forms mod p