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On a question of Mauri and Moraga

Jihao Liu

A surface qdlt log Calabi–Yau pair with three big boundary components has a square dual complex, rather than the boundary of a two-dimensional standard simplex. This answers part (2) of Mauri and Moraga’s Question 9.9 negatively.

Sources for this record

What was already known

Mauri and Moraga had shown the relevant dual complexes are PL-homeomorphic to spheres and asked for the stronger simplex-boundary conclusion.

AI involvement AI-autonomous

Jihao Liu credits ChatGPT 5.5 Pro with the part (2) example in one shot. Liu presented the argument; Kaiyuan Gu, Ruicheng Hu and Sheng Qin helped verify an earlier blueprint of unspecified scope.

The source explicitly identifies the assessed part (2) answer as a one-shot ChatGPT result after the human posed the question.

Importance Notable

Supplies a concrete counterexample to the simplex-boundary claim for surfaces.

Limitations

The distinct threefold non-qdlt example for part (1) needed a later repair and is outside this result. The acknowledged checking of an earlier blueprint is not clearly tied to the final surface example.

Technical verification Reported

The v1 paper supplies a short argument, but the acknowledged verification concerns an earlier blueprint of unspecified scope. No completed check of this final part (2) claim is documented; Reported is an evidence default.

Human understanding Few

Default for undocumented human understanding: the final proof is explained, but the source does not identify a human account of the one-shot model construction's mechanism or a scoped final review.

Correction and publication history