A virtual structure for symplectic Higgs bundles

2025/10/28 by Schirren, Simon
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.24531

Abstract

We define a perfect obstruction theory for a moduli of symplectic Higgs sheaves (E,ϕ) on projective surfaces S. Key to this is a minimality assumption on \textrmch(E) that forces all E to be locally free. This might have implications to define a virtual count and Sp(r)-Vafa-Witten invariants.

Citations

• Counting sheaves on Calabi-Yau 4-folds, I
• Moduli space of principal sheaves over projective varieties
• Localization of virtual classes

Related

• On the construction of moduli stack of projective Higgs bundles over\n surfaces
• A perfect obstruction theory for SU(2)-Higgs pairs
• Counting twisted sheaves and S-duality
• Symplectic resolutions for Higgs moduli spaces
• Localizing Virtual Structure Sheaves for Almost Perfect Obstruction Theories