2023/03/15 by Ana Peón‐Nieto, Peón-Nieto, Ana
Mathematics · #14H60 #14H70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2303.08563
openalex publication_date 2023/03/15 · openalex created_date 2023/03/18 · openalex updated_date 2026/07/28
We give a birational description of the reduced schemes underlying the irreducible components of the nilpotent cone and the \CC^×-fixed point locus of length two in the moduli space of Higgs bundles. Using these results, we prove Drinfeld's conjecture for the sublocus of type (n0,n1) fixed points. We introduce the notion of \U(n0,n1)-wobbliness (stronger than the one of wobbliness) and show that fixed point components of type (n0,n1) are wobbly in rank higher than three, if and only if they are also \U(n0,n1)-wobbly. This yields a computable criterion to check wobbliness of fixed point components, that simplifies the existing ones. We analyse the virtual equivariant multiplicities of fixed points of type (n0,n1) and their Euler pairings with downward flows for type (1,…, 1) fixed points. We find that both invariants fail to fully detect all wobbly components for ordered partitions other than (2,1).