Bibliographic record
Abstract
Let $X=\Gamma \backslash \mathbb{B}^{n} $ be an $n$-dimensional complex ball quotient by a torsion-free non-uniform lattice $\Gamma$ whose parabolic subgroups are unipotent. Let $\overline{X}$ be the unique toroidal complication of $X.$ In the first part of this thesis we prove positivity properties of $\Omega^{1}_{\overline{X}}$ and $\Omega^{1}_{\Xb}\big(\log(D)\big)$ depending intrinsically on $X$. We prove that $\Omega^{1}_{\Xb}\big(\log(D)\big) \langle} -r D \rangle}$ is ample for all sufficiently small rational numbers $r >0$, and $\Omega^{1}_{\Xb}\big(\log(D)\big)$ is ample modulo $D.$ Further, we conclude that if the cusps of $X$ have uniform depth greater than $4\pi$, then $\Omega^{1}_{\Xb}$ is semi-ample and is ample modulo $D$, and all subvarieties of $X$ are of general type. In the second part of this thesis we prove that the volumes of subvarieties of $X$ are controlled by the systole of $X,$ which is the length of the shortest closed geodesic of $X$. There are a number of arithmetic and geometric consequences: the systole of $X$ controls the growth rate of rational points on $X,$ uniformly in the field of definition of $\overline{X}.$ Also, we obtain effective global generation and very ampleness results for multiples of the canonical bundle $K_{\overline{X}}.$ These results follow from the bound we find for the Seshadri constant of $K_{\overline{X}}$ in terms of the systole.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".