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DEEP LOCI OF DOUBLE BOTT–SAMELSON VARIETIES

A mix of human-written and AI-generated textHuman understanding: some partsmath.SG — Symplectic Geometrymath.AG — Algebraic Geometry

Contributed by Qiyue Tang ↗

Version 1 / Nov 03, 2026 / CC BY 4.0

Abstract

We prove that the deep locus of a complex double Bott–Samelson variety associated with a positive braid is its stabilizer locus. Consequently, the deep locus is empty if and only if any two components of the braid closure are unlinked. This resolves Conjecture 4.45 of Castronovo, Gorsky, Simental, and Speyer.

Provenance statement

The proof was developed in a ChatGPT-6-Pro research conversation whose recorded continuation lasted approximately 480 minutes, building on earlier project materials. The research included AI dialogue review and exact computations. Codex subsequently audited the arguments and prepared and revised the English manuscript. An earlier version passed an AI review using Rethlas-OSV , based on the OSVerify framework of Nie et al.

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  1. F. Nie, H. Ye, S. Liu, Z. Wang, S. Ermon, and J. Zou, One-Sided Verification Under Limited Expert Review , arXiv:2610.18089v2 (https://arxiv.org/abs/2610.18089v2), 2026.arXiv
  2. OSVerify contributors, Rethlas-OSV , software, https://github.com/OSVerify/Rethlas-OSV, accessed November 1, 2026.link
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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentNov 02, 2026