{"id":"W3195842353","doi":"10.1016/j.aim.2021.108035","title":"The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.svg\"> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> </mml:math>","year":2021,"lang":"lv","type":"article","venue":"Advances in Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii; Agence Nationale de la Recherche; Ontario Ministry of Research, Innovation and Science; National Sleep Foundation; Corporation for National and Community Service; National Science Foundation","keywords":"Mathematics; Hypersurface; Polynomial; Combinatorics; Degree (music); Bounded function; Hessian matrix; Ideal (ethics); Algebra over a field; Pure mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002421836,0.0004110611,0.0003927535,0.001290366,0.000794509,0.001774098,0.0005974606,0.000350235,0.02031182],"category_scores_gemma":[0.0009127254,0.0002001485,0.0004355102,0.0006334568,0.001669551,0.002071264,0.0008690374,0.001613136,0.004639866],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001388146,"about_ca_system_score_gemma":0.0008772405,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.006685308,"about_ca_topic_score_gemma":0.004096698,"domain_scores_codex":[0.9996582,0.00004313373,0.00001037565,0.00006602574,0.0001547459,0.00006742784],"domain_scores_gemma":[0.9997188,0.00004789206,0.00003119744,0.0000327317,0.000095727,0.00007355775],"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":[0.00004214001,0.0000292093,0.0002578736,0.00004089054,0.000007477856,0.0001482845,0.0002557283,0.001919018,0.002791313,0.9721749,0.009861719,0.01247133],"study_design_scores_gemma":[0.0000352791,0.00005843902,0.002066189,0.00002521813,0.00001400303,0.0004255709,0.0003129,0.02576058,0.004336462,0.9212505,0.04566782,0.0000469375],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3044665,0.001294313,0.22294,0.005863034,0.001083473,0.0001293904,0.002566046,0.001104169,0.4605529],"genre_scores_gemma":[0.8439097,0.0007010004,0.02151477,0.0002842457,0.0005417247,0.00003995656,0.001540347,0.0005085122,0.1309598],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02031182,"threshold_uncertainty_score":0.06794983,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01722815847805714,"score_gpt":0.2584617818408843,"score_spread":0.2412336233628271,"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."}}