2001/04/06 by Andreas Rosenschon, Rosenschon, Andreas, Morihiko Saito +1
Computer Science · Mathematics · #14C25 #14C30 #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Complexity and Algorithms in Graphs #FOS: Mathematics #Interconnection Networks and Systems #math.AG #msc:14C25 #msc:14C30
paper · pdf · doi:10.48550/arxiv.math/0104079
AMS-TeX, 17 pages, Introduction and Sect. 1 changed
openalex publication_date 2001/04/06 · arxiv created 2001/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a class of cycles, called nondegenerate, strictly decomposable cycles, and show that the image of each cycle in this class under the refined cycle map to an extension group in the derived category of arithmetic mixed Hodge structures does not vanish. This class contains certain cycles in the kernel of the Abel-Jacobi map. The construction gives a refinement of Nori's argument in the case of a self-product of a curve. As an application, we show that a higher cycle which is not annihilated by the reduced higher Abel-Jacobi map produces uncountably many indecomposable higher cycles on the product with a variety having a nonzero global 1-form.