Statements (18)
| Predicate | Object | 
|---|---|
| gptkbp:instanceOf | 
                                    
                                        
                                            gptkb:mathematical_concept
                                        
                                         | 
                            
| gptkbp:appliesTo | 
                                    
                                        
                                            
                                            linear systems
                                        
                                        
                                         projective varieties  | 
                            
| gptkbp:field | 
                                    
                                        
                                            gptkb:algebraic_geometry
                                        
                                         | 
                            
| gptkbp:generalizes | 
                                    
                                        
                                            
                                            generic smoothness theorem
                                        
                                        
                                         | 
                            
| gptkbp:hasVariant | 
                                    
                                        
                                            gptkb:Bertini's_irreducibility_theorem
                                        
                                         Bertini's theorem on irreducibility  | 
                            
| gptkbp:namedAfter | 
                                    
                                        
                                            gptkb:Eugenio_Bertini
                                        
                                         | 
                            
| gptkbp:publishedIn | 
                                    
                                        
                                            gptkb:Annali_di_Matematica_Pura_ed_Applicata
                                        
                                         | 
                            
| gptkbp:relatedTo | 
                                    
                                        
                                            
                                            base locus
                                        
                                        
                                         generic smoothness hyperplane section  | 
                            
| gptkbp:sentence | 
                                    
                                        
                                            
                                            A general member of a linear system on a smooth variety is smooth outside the base locus.
                                        
                                        
                                         A general hyperplane section of a smooth projective variety is smooth.  | 
                            
| gptkbp:yearProposed | 
                                    
                                        
                                            
                                            1882
                                        
                                        
                                         | 
                            
| gptkbp:bfsParent | 
                                    
                                        
                                            gptkb:Poonen's_Bertini_theorem
                                        
                                         | 
                            
| gptkbp:bfsLayer | 
                                    
                                        
                                            
                                            7
                                        
                                        
                                         | 
                            
| https://www.w3.org/2000/01/rdf-schema#label | 
                                    
                                        
                                            
                                            Bertini's theorem
                                        
                                        
                                         |