{"id":"W2899110854","doi":"10.1016/j.aim.2023.108931","title":"A Riemann-Hurwitz-Plücker formula","year":2023,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Windsor","funders":"Natural Sciences and Engineering Research Council of Canada; Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada; Simons Foundation","keywords":"Mathematics; Inflection point; Morphism; Pure mathematics; Projective variety; Algebraic curve; Variety (cybernetics); Riemann–Hurwitz formula; Generalization; Algebraic variety; Riemann hypothesis; Algebraic number; Projective test; Degeneracy (biology); Mathematical analysis; Geometry; Riemann Xi function","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000507326,0.0007842993,0.0006834578,0.001606039,0.001394455,0.002625405,0.00108219,0.001445726,0.01210918],"category_scores_gemma":[0.002091906,0.000284823,0.0005111356,0.001615531,0.002153425,0.004151084,0.002013474,0.002298267,0.002137791],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001094901,"about_ca_system_score_gemma":0.00058516,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008687352,"about_ca_topic_score_gemma":0.0005744912,"domain_scores_codex":[0.999663,0.00008362521,0.00001441064,0.00006935009,0.0001131117,0.00005648375],"domain_scores_gemma":[0.9996301,0.0001038081,0.00003336543,0.00005900534,0.0001054313,0.00006821644],"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":[0.000009799981,0.000006516575,0.00005856121,0.0000132744,0.000002645923,0.00004063777,0.00006049815,0.0001712922,0.0003582312,0.9936579,0.001420238,0.004200506],"study_design_scores_gemma":[0.000006453355,0.000006100551,0.0001184896,0.000006456753,0.000003640361,0.00008805213,0.00003212296,0.001558557,0.0002644708,0.9934737,0.004435476,0.000006431973],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2514604,0.004626399,0.1821779,0.009488958,0.002507707,0.00007940773,0.0006620596,0.0007086841,0.5482885],"genre_scores_gemma":[0.9112411,0.001442551,0.01960021,0.0008808599,0.001150304,0.00004516226,0.0002873672,0.0001818391,0.06517064],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01210918,"threshold_uncertainty_score":0.04050928,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02864871067093334,"score_gpt":0.3381458027741914,"score_spread":0.3094970921032581,"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."}}