Universal-cover convexity counterexample library

Family 046: Shafarevich counterexamples in dimension two and with large fundamental group. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Prevent researchers from inferring Stein or holomorphic convexity solely from a large fundamental group and absence of compact positive-dimensional analytic subspaces.

Applicability and commercial boundary

The specific projective fourfold and surface examples do not rule out convexity in all restricted geometries.

Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

Next verification action

Extract an explicit counterexample and each implication it refutes.

Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

A projective fourfold with large fundamental group and non-Stein universal cover.