{"id":"W4318193147","doi":"10.1007/s10801-022-01201-7","title":"On generators and relations of the rational cohomology of Hilbert schemes","year":2023,"lang":"en","type":"article","venue":"Journal of Algebraic Combinatorics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"H2020 European Research Council; Danmarks Grundforskningsfond; National Research Foundation; European Commission","keywords":"Mathematics; Moduli space; Cohomology; Multiplicative function; Combinatorics; Degree (music); Boundary (topology); Commutative property; Algebra over a field; Discrete mathematics; Pure mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004483723,0.00008807248,0.0002551749,0.000177704,0.0001064378,0.000006892229,0.000216353,0.00006267898,0.00004649236],"category_scores_gemma":[0.001056924,0.00006201656,0.0001097666,0.0006653245,0.0001416859,0.00006700716,0.00008529486,0.0002182858,0.00000297482],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003465137,"about_ca_system_score_gemma":0.0001439768,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000160914,"about_ca_topic_score_gemma":0.000001994466,"domain_scores_codex":[0.9988589,0.000100153,0.0005568517,0.00007365554,0.0003184785,0.00009193017],"domain_scores_gemma":[0.9970644,0.001612559,0.0006654799,0.0002220772,0.0003915654,0.000043949],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001002995,0.000132693,0.004687247,0.00002210895,0.00007442259,8.777333e-7,0.000405149,0.00001496178,0.00120502,0.984285,0.009001825,0.0001606935],"study_design_scores_gemma":[0.0005284988,0.0001687594,0.02701104,0.00004318873,0.0000616117,0.00002008234,0.0001076908,0.0001285911,0.004327749,0.9667205,0.0008228852,0.00005938799],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9964244,0.0001300701,0.0004179123,0.002039057,0.0002181944,0.0001199691,0.000007621205,0.000008046872,0.0006346702],"genre_scores_gemma":[0.9991162,0.00004584578,0.0004767769,0.00004159248,0.0000286649,0.000003720703,0.000001284548,0.00001161445,0.000274281],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0223238,"threshold_uncertainty_score":0.2528962,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0280525998320959,"score_gpt":0.2991745006000202,"score_spread":0.2711219007679243,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}