Bibliographic record
Abstract
In the first part of this thesis we study the cohomology of broken toric varieties via the derived push-forward of the constant sheaf to a complex of polytopes, using it to prove a Deligne-type decomposition theorem and degeneration of the associated Leray-Serre spectral sequence. We discuss certain maps between broken toric varieties and how they descend to maps of cohomology groups. Furthermore, we give a description of the Betti numbers of some broken toric varieties whose associated complex of polytopes is the n-skeleton of a higher dimensional polytope, encompassing some important examples. In the second part we investigate hypertoric Hitchin systems, whose cohomology is governed by a subvariety which is broken toric. After reviewing their construction, we give a new proof of a deletion-contraction relationship on these varieties (first proven by Dansco-McBreen-Shende) and refine it to a statement about the cohomology of certain sheaves on the polytopal complex. Using these facts and the general results in the first part of the thesis, we develop tools for calculating the cohomology of some families of hypertoric Hitchin systems inductively, given knowledge of some base cases. In particular, this yields explicit formulae for the Poincaré polynomials of hypertoric Hitchin systems associated to graphs with first Betti number 2.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 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 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".