A slope-unstable bundle on a surface with 1-homogeneous projectivization

Jihao Liu

Abstract

We answer affirmatively a question of Fulger and Langer on the interplay between slope semistability and positivity for projective bundles with vanishing discriminant. The main result of this paper was obtained by Chatgpt 5.5 pro, and the Danus system based on the Rethlas system.

Disclosure

“ndependent, nef, and non-big, so they span both the nef cone and the pseudo-effective cone. This two-ray cone argument is mentioned in [FL22, Remark 4.2]. Remark 1.5. The sketch of the proof of the main result of this paper was obtained by Chatgpt 5.5 pro, and later summed up, verified, and properly written by the Danus system, a specialized agent built on Rethlas and substantially more capable for fundamental mathematical research based on the Rethlas system. Human verification and”
PDF page 2

Classification: Substantial proof generation
Multiplier: 10
Verified: 2026-08-24T00:34:05.733Z

Structural counts

Pages 5 pdf

Theorems 2 source

Lemmas 4 source

Propositions 2 source

Corollaries 0 source

Definitions 0 source

Displayed equations 19 source

Bibliography entries 4 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Slope_FL22_v2.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.