A surface counterexample to Shafarevich holomorphic convexity

Related prior literature mentioned by others

• Fedor Bogomolov and Ludmil Katzarkov, Complex projective surfaces and infinite groups (arXiv:alg-geom/9703002, 1997). The AI Proved What? exposition identifies this construction of potential Shafarevich counterexamples, conditional on group-theoretic questions, as a predecessor to the two manuscripts. [family-level]
• Philippe Eyssidieux, Ludmil Katzarkov, Tony Pantev and Mohan Ramachandran, Linear Shafarevich conjecture (Annals of Mathematics 176, 2012). The AI Proved What? exposition contrasts the manuscripts' unrestricted fundamental groups with this affirmative holomorphic-convexity theorem for projective manifolds with linear fundamental groups. [family-level]

Possibly relevant literature (found by the agent, not checked)

• Ya Deng, Topology, Hyperbolicity, and the Shafarevich Conjecture for Complex Algebraic Varieties (arXiv:2512.24458, December 2025). A recent survey whose §1.2.1 describes the Shafarevich conjecture as open in full generality; it gives background on the status of the conjecture that this paper's Theorem 1.1 addresses.
• Rodolfo Aguilar and Cristhian Garay, A Real Shafarevich Conjecture for Universal Covers (arXiv:2603.17939, March 2026). Proposes a refinement of the complex holomorphic-convexity conjecture for varieties defined over the reals and proves it for curves and nilpotent fundamental groups; this paper's Theorem 1.1 bears on the complex statement that the refinement starts from.
• Benjamin Bakker, Non-abelian Hodge theory for non-proper varieties and the linear Shafarevich conjecture (arXiv:2603.23467, March 2026; ICM 2026 proceedings). An exposition of the linear Shafarevich conjecture for arbitrary algebraic varieties; it relates to this paper's deduction that the surface's fundamental group has no faithful finite-dimensional complex representation.
• Yuan Liu, On the holomorphic convexity of nilpotent coverings over compact Kähler surfaces (arXiv:2411.15744, 24 November 2024). Its holomorphic-convexity theorem for nilpotent regular covers without two ends provides an additional comparison for the manuscript's surface counterexample and its discussion of positive results under fundamental-group restrictions.

Digests and expositions

• AI Proved What?, Shafarevich refuted? Counterexamples to holomorphic convexity (Episode 046, October 2026). This AI-assisted video and transcript explain both the surface's infinite chain of rational curves and the fourfold's lifted abelian-surface obstruction, with outlines of the two constructions. [AI-generated per source] [family-level]

News and blogs

• Ben Laufer, OpenAI's most cited mathematician is OpenAI. (Substack "Applied Overthinking", 2026-10-08). A citation-network analysis of the release that uses this paper as node A of a citation cycle with the semialgebraic-covers and abelianity manuscripts; the author states that the papers were not read and that a citation cycle does not establish a circular proof.