Big monodromy for higher Prym representations
Bibliographic record
Abstract
Let † g 0 !† g be a cover of an orientable surface of genus g by an orientable surface of genus g 0 , branched at n points, with Galois group H .Such a cover induces a virtual action of the mapping class group Mod g;nC1 of a genus g surface with n C 1 marked points on H 1 .† g 0 ; C/.When g is large in terms of the group H , we calculate precisely the connected monodromy group of this action.The methods are Hodge-theoretic and rely on a "generic Torelli theorem with coefficients".14H30; 14D07, 14H10, 14H40, 14H60, 57K20 1. Introduction 2733 2. Notation and preliminaries on moduli 2742 3. Review of parabolic bundles and period maps 2745 4. Global generation of vector bundles on generic curves 2747 5. Preliminaries on variations of Hodge structure 2752 6. Generic Torelli theorems for unitary local systems 2756 7. Big monodromy for g large 2760 8. Big monodromy for n large 2771 9. Big monodromy for Kodaira fibrations 2773 10.Questions 2778 References 27791 .† g;n ; x/ H .The stabilizer Mod ' Mod g;nC1 of ' acts on the kernel K of '.The induced action on K ab D H 1 .† g 0 ;n 0 ; Z/ preserves the kernel of the natural morphismand thus ' gives rise to a virtual action of Mod g;nC1 on H 1 .† g 0 ; Z/, ie an action of Mod ' on H 1 .† g 0 ; Z/.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".