Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complex affine space
|
| gptkbp:discusses |
gptkb:Mathematical_Reviews
gptkb:Encyclopedia_of_Mathematics arXiv preprints |
| gptkbp:field |
gptkb:algebraic_geometry
polynomial mappings |
| gptkbp:hasMSCClassification |
gptkb:14E07
gptkb:14R15 |
| gptkbp:hasPartialResults |
true for n = 1
true for certain classes of polynomials |
| https://www.w3.org/2000/01/rdf-schema#label |
The Jacobian conjecture
|
| gptkbp:notableFor |
being unsolved for n > 1
|
| gptkbp:proposedBy |
gptkb:Ott-Heinrich_Keller
|
| gptkbp:relatedTo |
gptkb:Keller's_Jacobian_problem
inverse function theorem polynomial automorphisms |
| gptkbp:sentence |
If a polynomial map from C^n to C^n has a constant nonzero Jacobian determinant, then the map is invertible and its inverse is also a polynomial map.
|
| gptkbp:status |
open problem
|
| gptkbp:yearProposed |
1939
|
| gptkbp:bfsParent |
gptkb:Mathematical_problems_for_the_next_century
|
| gptkbp:bfsLayer |
6
|