Metric wall crossing in rank-three K3 bundle moduli

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-06
DOI
https://doi.org/10.5281/zenodo.24021821
Primary Topic
Geometry and complex manifolds
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
preprint

Metric wall crossing in rank-three K3 bundle moduli

Bernd Johannes Wuebben
2 links
Zenodo (CERN European Organization for Nuclear Research)
Geometry and complex manifolds
preprint

Metric wall crossing in rank-three K3 bundle moduli

Bernd Johannes Wuebben
preprint en

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.

Zenodo (CERN European Organization for Nuclear Research)
Geometry and complex manifolds
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon
Metric wall crossing in rank-three K3 bundle moduli — Bernd Johannes Wuebben · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS