On the Chern filtration for the moduli of bundles on curves

2024/10/31 by Woonam Lim, Lim, Woonam, Miguel Moreira +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.24008

openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study the Chern filtration on the cohomology of the moduli of bundles on curves. This can be viewed as a natural cohomological invariant defined via tautological classes that interpolates between additive Betti numbers and the multiplicative ring structure. In the rank two case, we fully compute the Chern filtration for moduli of stable bundles and all intermediate stacks in the Harder--Narasimhan stratification. We observe a curious symmetry of the Chern filtration on the moduli of rank two stable bundles, and construct \mathfraksl₂-actions that categorify this symmetry. Our study of the Chern filtration is motivated by the P=C phenomena in several related geometries.

Related

• Universal Chern classes on the moduli of bundles
• The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves
• Chern Classes of the Moduli Stack of Curves
• The Chern character of the Verlinde bundle over the moduli space of stable curves
• Geometry of the intersection ring and vanishing relations in the\n cohomology of the moduli space of parabolic bundles on a curve