Hodge cycles on some moduli spaces

2001/02/08 by Donu Arapura, Arapura, Donu · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0102070

28 pages latex; This is a major revision with new material on generalized Hodge conjecture and moduli of bundles over abelian and K3 surfaces

openalex publication_date 2001/02/08 · arxiv created 2002/08/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface or a curve if it holds for all powers of the surface or curve. In the latter case, the curve can be replaced by its Jacobian. As a consequence the generalized Hodge conjecture holds for these moduli spaces when the curve is very general. A similar result is proved for the Hilbert schemes of points over an arbitrary surface.

Cited by

• Functoriality of the coniveau filtration
• Motivic integration and projective bundle theorem in morphic cohomology

Related

• Motivation for Hodge cycles
• Hodge numbers of moduli spaces of stable bundles on K3 surfaces
• The motive of some moduli spaces of vector bundles over a curve
• K3 surfaces associated with varieties of generalized Kummer type
• G-bundles on Abelian surfaces, hyperkahler manifolds, and stringy Hodge numbers