Modularity of Landau–Ginzburg Models
Bibliographic record
Abstract
For each smooth Fano threefold, we construct a family of Landau–Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry. These Landau–Ginzburg models are log Calabi–Yau varieties with proper superpotential maps; they admit open algebraic torus charts on which the superpotential function $$\mathsf{w}$$ restricts to a Laurent polynomial satisfying a deformation of the Minkowski ansatz; and the general fibres of $$\mathsf{w}$$ are Dolgachev–Nikulin dual to the anticanonical hypersurfaces in the initial Fano threefold. To construct the family of models, we develop the deformation theory of Landau–Ginzburg models in arbitrary dimension, following the work of Katzarkov, Kontsevich, and Pantev (2017), with special emphasis on the case of Landau–Ginzburg models obtained from Laurent polynomials. Our proof of the Dolgachev–Nikulin mirror symmetry is by detailed case-by-case analysis, which refines Cheltsov and Przyjalkowski’s work (published in the same volume of the journal) on the verification of the Katzarkov–Kontsevich–Pantev conjecture.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".