Partial desingularization
Bibliographic record
Abstract
We address the following question of partial desingularization preserving normal crossings . Given an algebraic (or analytic) variety X X in characteristic zero, can we find a finite sequence of blowings-up preserving the normal-crossings locus of X X , after which the transform X ′ X’ of X X has only singularities from an explicit finite list of minimal singularities , which we define using the determinants of circulant matrices. In the case of surfaces, for example, the pinch point or Whitney umbrella is the only singularity needed in addition to normal crossings. We develop techniques for factorization (splitting) of a monic polynomial with regular (or analytic) coefficients, satisfying a generic normal crossings hypothesis, which we use together with resolution of singularities techniques to find local circulant normal forms of singularities. These techniques in their current state are enough for a positive answer to the question above, for dim X ≤ 4 \dim X \leq 4 , or in arbitrary dimension if we preserve normal crossings only of order at most three. In these cases, minimal singularities have smooth normalization.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.002 |
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".