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What (who) is Jacobian - definition
Jacobian
WIKIMEDIA DISAMBIGUATION PAGE
Jacobian (disambiguation)
·adj Of or pertaining to a style of architecture and decoration in the time of James the First, of England.
Jacobian variety
MODULI SPACE OF DEGREE 0 LINE BUNDLES ON A CURVE; THE IDENTITY COMPONENT OF THE PICARD GROUP
Jacobian varieties; Jacobi variety; Jacobian of a curve
In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of C, hence an abelian variety.
Jacobian conjecture
CONJECTURE ASSERTING THAT, OVER A CHARACTERISTIC-ZERO FIELD K, GIVEN A POLYNOMIAL MAP F: Kⁿ → Kⁿ, IF ITS JACOBIAN DETERMINANT J: Kⁿ → K IS A NONZERO CONSTANT MAP, THEN F ADMITS A POLYNOMIAL INVERSE G: Kⁿ → Kⁿ
Keller's problem; Smale's sixteenth problem; Jacobian problem
In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an n-dimensional space to itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse.
