Exact 2-Adic Monodromy in a Genus-Three Two-Pair Pencil: Congruence Strata and Geometric Meridians
Year: 2026
Type: preprint
Abstract: We study the genus-three hyperelliptic pencil y²=(z+5)(z+3)(z−x)(z−6)(z²−t²)((z−1)²−4t²), excluding fixed-root degeneracies x=−5,−3,6. We prove full connected Sp6 Zariski monodromy and classify the 2-adic closure H_x of integral geometric monodromy by K₂⊂H_x⊂K₁ and exact indices 16, 32, 64, and 128. The proof combines genuine collision meridians, a seven-vertex sufficient condition, a unimodular x=5 packet certificate, independently checked Burau transport, an integral triple-root local model, and finite first-bracket congruence certificates. At each parameter stratum we supply explicit mod-four image data and reproducible Research/QA code. This bibliographic revision adds references to earlier related Zenodo preprints on weighted genus-two pencils, reflection symmetry, and a different genus-three two-moving-pair pencil; the results and finite certificates are unchanged. Geometric identifications use classical branched-cover/Picard–Lefschetz theory. This is a research preprint, not externally refereed.
Author: Lee, Byoungwoo
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225646937