Normal forms and Tyurin degenerations of K3 surfaces polarized by a rank 18 lattice
Bibliographic record
Abstract
Abstract We study projective Type II degenerations of K3 surfaces polarized by a certain rank 18 lattice, where the central fiber consists of a pair of rational surfaces glued along a smooth elliptic curve. Given such a degeneration, one may construct other degenerations of the same kind by flopping curves on the central fiber, but the degenerations obtained from this process are not usually projective. We construct a series of examples which are all projective and which are all related by flopping single curves from one component of the central fiber to the other. Moreover, we show that this list is complete, in the sense that no other flops are possible. The components of the central fibers obtained include weak del Pezzo surfaces of all possible degrees. This shows that projectivity need not impose any meaningful constraints on the surfaces that can arise as components in Type II degenerations.
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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 | 0.001 | 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 | 0.000 | 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".