Metric wall crossing in rank-three K3 bundle moduli
Year: 2026
Type: preprint
Abstract: We determine the local harmonic L² metric near a stability wall in a complex twelve-dimensional moduli space of rank-three bundles on a projective K3 surface. The central bundle is the sum of two copies of one spherical line bundle and a second spherical line bundle, with five-dimensional cross-extension spaces; the central Kähler metric is Ricci-flat. We compare the actual chamber metrics with the standard hyperkähler quotient metrics on T*Gr(2,5) and T*Gr(3,5), with relative error quadratic in the deformation size. The comparison is uniform through changes of stabilizer and permits unrelated rates of approach to the wall and its singular strata. It gives the exceptional-fibre collapse scale, complete pointed Gromov–Hausdorff limits after rescaling, quantitative matching to the wall metric, and intrinsic distance asymptotics to the contracted loci. The proof corrects the real moment equation within complex orbits with a bound that remains uniform at the reducible strata.
Author: Wuebben, Bernd Johannes
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225410422