mathematics, the intermediate Jacobian of a compact Kähler manifold or Hodge structure is a complex torus that is a common generalization of the Jacobian variety...

variety, the Albanese variety, generalized Jacobian, and intermediate Jacobians are generalizations of the Jacobian for higher-dimensional varieties. For varieties...

the robot Jacobian) Jacobian elliptic functions Jacobian variety Jacobian ideal Intermediate Jacobian This set index article includes a list of related...

In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order...

geometric statement of Jacobi Generalized Jacobian Intermediate Jacobian Jacobian conjecture Jacobian curve Jacobian matrix and determinant Jacobian variety...

that unirationality does not imply rationality. Their work used an intermediate Jacobian. Iskovskih & Manin (1971) showed that all non-singular quartic threefolds...

{\displaystyle A(V)} , named for Giacomo Albanese, is a generalization of the Jacobian variety of a curve. The Albanese variety of a smooth projective algebraic...

algebraic varieties that includes both ordinary cohomology and intermediate Jacobians. For introductory accounts of Deligne cohomology see Brylinski (2008...

S2CID 3342362 Clemens, C. Herbert; Griffiths, Phillip A. (1972), "The intermediate Jacobian of the cubic threefold", Annals of Mathematics, Second Series, 95...

Abel–Jacobi map from cycles homologically equivalent to zero to the intermediate Jacobian. The exponential sequence shows that CH1(X) maps isomorphically...

MR 0233814. Clemens, C. Herbert; Griffiths, Phillip A. (1972). "The intermediate Jacobian of the cubic threefold". Annals of Mathematics. 95 (2): 281–356...

threefolds are all unirational, but Clemens & Griffiths (1972) used intermediate Jacobians to show that non-singular cubic threefolds are not rational. The...

this presheaf over the previous site. Spectral algebraic geometry Intermediate Jacobian Chromatic homotopy theory Goerss, Paul G. (2009-05-08). "Realizing...

thesis advisor Frans Oort and thesis Limits of Hodge Structures and Intermediate Jacobians. He is now a professor at Radboud University Nijmegen. His research...

restrictions. Poincare bundle Complex Lie group Automorphic function Intermediate Jacobian Elliptic gamma function Mumford, David (2008). Abelian varieties...

information about the kernel of the cycle map, for example using the intermediate Jacobians which are built from the Hodge structure. Mixed Hodge theory, developed...

C. Bose National Fellowship in 2009. Balaji, V (August 1990). "Intermediate Jacobian of Some Moduli Spaces of Vector Bundles on Curves". American Journal...

dimension, by replacing "derivative" with "Jacobian matrix" and "nonzero derivative" with "nonzero Jacobian determinant". If the function of the theorem...

endomorphism. This is used in calculus with exterior differential forms and the Jacobian determinant, in particular for changes of variables in multiple integrals...

; Morrey, Charles B. Jr. (1985). "Implicit Function Theorems. Jacobians". Intermediate Calculus (2nd ed.). New York: Springer. pp. 390–420. ISBN 0-387-96058-9...

1940 André Weil defines "abelian variety" 1952 Weil defines an intermediate Jacobian Theorem of the cube Selmer group Michael Atiyah classifies holomorphic...

MR 0212019 Clemens, C. Herbert; Griffiths, Phillip A. (1972), "The intermediate Jacobian of the cubic threefold", Annals of Mathematics, Second Series, 95...

519-567 (with V. Gritsenko, G. K. Sankaran) The class of the locus of intermediate Jacobians of cubic threefolds, Invent. Math. 190 (2012), No. 1, 119-168 (with...

total derivative is called a Jacobian matrix, and the composite of two derivatives corresponds to the product of their Jacobian matrices. From this perspective...

curvilinear change of coordinates, it transforms by the reciprocal of the Jacobian of the coordinate change. For more on the intrinsic meaning, see Density...

{\frac {\|J(x)\|}{\|f(x)\|/\|x\|}},} where ⁠ J ( x ) J(x) ⁠ denotes the Jacobian matrix of partial derivatives of f {\displaystyle f} at x {\displaystyle...

partial derivatives exist at x0, and the linear map J is given by the Jacobian matrix, an n × m matrix in this case. A similar formulation of the higher-dimensional...

)}\operatorname {sgn} \det(Df(y))} , where D f ( y ) {\displaystyle Df(y)} is the Jacobian matrix, 0 = ( 0 , 0 , . . . , 0 ) T {\displaystyle \mathbf {0} =(0,0,....

gradients. Unlike modern backpropagation, these precursors used standard Jacobian matrix calculations from one stage to the previous one, neither addressing...

instead has to left multiply the function F(xn) by the inverse of its k × k Jacobian matrix JF(xn). This results in the expression x n + 1 = x n − J F ( x n...