Bibliographic record
Abstract
Minimal graded free resolutions are an important and central topic in algebra. They are a useful tool for studying modules over finitely generated graded K- algebras. Such a resolution determines the Hilbert series, the Castelnuovo-Mumford regularity and other invariants of the module. This thesis is concerned with the structure of minimal graded free resolutions. We relate our results to several recent trends in commutative algebra. The first of these trends deals with relations between properties of the Stanley- Reisner ring associated to a simplicial complex and the Stanley-Reisner ring of its Alexander dual. Another development is the investigation of the linear part of a minimal graded free resolution as defined by Eisenbud and Schreyer. Several authors were interested in the problem to give lower bounds for the Betti numbers of a module. In particular, Eisenbud-Koh, Green, Herzog and Reiner- Welker studied the graded Betti numbers which determine the linear strand of a minimal graded free resolution. Bigraded algebras occur naturally in many research areas of commutative algebra. A typical example of a bigraded algebra is the Rees ring of a graded ideal. Herzog and Trung used this bigraded structure of the Rees ring to study the Castelnuovo- Mumford regularity of powers of graded ideals in a polynomial ring. Conca, Herzog, Trung and Valla dealt with diagonal subalgebras of bigraded algebras. Aramova, Crona and De Negri studied homological properties of bigraded K-algebras.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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".