Integral reconstruction and quantitative metric degeneration of K3 bundle moduli
Year: 2026
Type: preprint
Abstract: We construct a compact moduli eightfold of rank-seven bundles on a K3 surface whose moving projective lines specialize to Schubert lines in a deepest Grassmannian fibre Gr(2,4). Both middle Schubert classes extend integrally. The fibre is primitive, has self-intersection six, and has an explicit degree-eight attachment modulo six. For the natural L² metric defined by harmonic deformation representatives, these same cycles have exact periods and volumes, ambient diameter asymptotics, and complete cotangent-Grassmannian rescaled limits. We also prove a global comparison theorem for compact K3 bundle-moduli contractions without bubbling, with complete convergent quiver charts whose complex moment-zero fibres contain simple representations. A principal-stratum path argument identifies the central harmonic completion, and finite quotient distances give a variational bound for the distortion of the actual contraction graph. The bound tends to zero through arbitrary adjacent chambers. Integral cochains on all geometric overlaps recover additive cohomology, while universal-index restrictions calculate middle-degree attachments from a marked complement ring. A mapping-torus example shows why local fibre rings and divisor classes do not determine the required monodromy.
Author: Wuebben, Bernd Johannes
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225589467