Lines on the Dwork pencil of quintic threefolds
Bibliographic record
Abstract
We present an explicit parameterization of the families of lines of the Dwork pencil of quintic threefolds.This gives rise to isomorphic curves C ±ϕ , which parameterize the lines.These curves are 125:1 covers of genus six curves C ±ϕ .The C ±ϕ are first presented as curves in P 1 ×P 1 that have three nodes.It is natural to blow up P 1 ×P 1 in the three points corresponding to the nodes in order to produce smooth curves.The result of blowing up P 1 ×P 1 in three points is the quintic del Pezzo surface dP 5 , whose automorphism group is the permutation group S 5 , which is also a symmetry of the pair of curves C ±ϕ .The subgroup A 5 , of even permutations, is an automorphism of each curve, whereas the odd permutations
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".