Lattice Moduli and Residual Atoms
Abstract
We study prescribed holomorphic lattices for regular-singular connections and residual factors of quantum F-bundles. For an arbitrary ordered monodromy spectrum, we classify the fully framed local groupoid: each residue fibre is a discrete affine space of dimension r(r−1), with a unique normal form and trivial stabilisers. We then analyse elementary changes of lattice. A strictly positive integral residue difference obstructs the oriented wall; otherwise, in arbitrary rank, the extending normal-form arcs form an affine torsor of relative dimension r(r−1), and specialisation to the shifted residue slice is polynomial and triangular by root height. Adjacent walls exhibit the composite-root correction dictated by the type-A root-subgroup relations, while an example over the dual numbers detects a nilpotent saturation defect. For one-branch F-bundles, the scalar branch is recovered from the residual trace, and scalar residualisation yields a symmetric monoidal equivalence with zero-branch F-bundles. This construction yields residual atoms, functorial Jordan strata, and a residual chemical formula compatible with blow-ups and projective bundles. In the A-model, residualisation removes the unit direction; the rationally marked large-radius residual germ recovers the divisor cubic and distinguishes the marked residual germs of the Pfaffian and Grassmannian Calabi--Yau threefolds.
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BibTeX
@misc{correa2026lattice,
title = {{Lattice Moduli and Residual Atoms}},
author = {Mauricio Corrêa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27723},
eprint = {2610.27723},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27723},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Lattice Moduli and Residual Atoms
AU - Mauricio Corrêa
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27723
UR - https://arxiv.org/abs/2610.27723
AB - We study prescribed holomorphic lattices for regular-singular connections and residual factors of quantum F-bundles. For an arbitrary ordered monodromy spectrum, we classify the fully framed local groupoid: each residue fibre is a discrete affine space of dimension r(r−1), with a unique normal form and trivial stabilisers. We then analyse elementary changes of lattice. A strictly positive integral residue difference obstructs the oriented wall; otherwise, in arbitrary rank, the extending normal-form arcs form an affine torsor of relative dimension r(r−1), and specialisation to the shifted residue slice is polynomial and triangular by root height. Adjacent walls exhibit the composite-root correction dictated by the type-A root-subgroup relations, while an example over the dual numbers detects a nilpotent saturation defect. For one-branch F-bundles, the scalar branch is recovered from the residual trace, and scalar residualisation yields a symmetric monoidal equivalence with zero-branch F-bundles. This construction yields residual atoms, functorial Jordan strata, and a residual chemical formula compatible with blow-ups and projective bundles. In the A-model, residualisation removes the unit direction; the rationally marked large-radius residual germ recovers the divisor cubic and distinguishes the marked residual germs of the Pfaffian and Grassmannian Calabi--Yau threefolds.
ER -