Infinitesimal invariant and vector bundles

2006/12/28 by Gian Pietro Pirola, Pirola, Gian Pietro, Cecilia Rizzi +1
Mathematics · Physics and Astronomy · #14 C15 #14C25 #14H40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AG #msc:14 #msc:14C25 #msc:14H40 #msc:C15

paper · pdf · doi:10.48550/arxiv.math/0612813

17 pages; accepted for pubblication in Nagoya Math. Journal

arxiv created 2006/12/28 · openalex publication_date 2006/12/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Saito-Ikeda infinitesimal invariant of the ccle defined by curves in their jacobians using rank (k+1) vector bundles and we give a criterion for which the higher cycle class map is not trivial. When k=2, this turns out to be strictly linked to the Petri map for vector bundles: an explicit construction on a curve of genus g>9 shows the existence of a non trivial element in the higher Griffiths group.

Related

• Cycles in Jacobians: infinitesimal results
• Higher Abel-Jacobi Maps
• Ranks of maps of vector bundles
• The Abel-Jacobi isomorphism on one cycles on the moduli space of vector bundles with trivial determinant on a curve
• On the vector bundles from Chang and Ran's proof of the unirationality of M_g, g ≤ 13