{"id":"W4391493003","doi":"10.1007/s00229-023-01530-2","title":"Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces","year":2024,"lang":"en","type":"article","venue":"manuscripta mathematica","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Hilbert's syzygy theorem; Mathematics; Vector bundle; Moduli space; Iterated function; Pure mathematics; Projective variety; Moduli; Algebraic geometry; Mathematical analysis; Physics","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":[0.001311003,0.0002545682,0.0006779302,0.0001835397,0.00006131602,0.00004499805,0.0002595672,0.0001082758,0.000303566],"category_scores_gemma":[0.0007444767,0.0001677095,0.0001185113,0.0003545556,0.0003474484,0.0001856863,0.0001342849,0.0001360356,0.00001388817],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002045783,"about_ca_system_score_gemma":0.00007525054,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006409228,"about_ca_topic_score_gemma":0.00001008087,"domain_scores_codex":[0.9979845,0.0001458573,0.0007865743,0.0003237538,0.0005336301,0.0002256735],"domain_scores_gemma":[0.9980457,0.0008706513,0.000298282,0.0005259103,0.0001933263,0.00006607789],"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":[0.0001063981,0.0009383044,0.0006080153,0.013083,0.0003412609,0.000003827382,0.003598289,0.00001984777,0.0081895,0.967976,0.004584564,0.0005510211],"study_design_scores_gemma":[0.0003048476,0.0003247544,0.00069537,0.00132157,0.0002039171,0.00001822941,0.002366018,0.002430746,0.06360692,0.927673,0.0007825237,0.0002721359],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9804988,0.001461087,0.002897378,0.0004161852,0.0001520263,0.0004877137,0.00009598874,0.00006932126,0.01392149],"genre_scores_gemma":[0.9792854,0.00008235822,0.01240796,0.00001511327,0.00002926185,0.00002021078,0.000005886333,0.00003672542,0.00811714],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05541742,"threshold_uncertainty_score":0.6838996,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06026455287918753,"score_gpt":0.2873884748288894,"score_spread":0.2271239219497018,"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."}}