In 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 of a curve and the Picard variety and the Albanese variety. It is obtained by putting a complex structure on the torus for n odd. There are several different natural ways to put a complex structure on this torus, giving several different sorts of intermediate Jacobians, including one due to André Weil and one due to Phillip Griffiths . The ones constructed by Weil have natural polarizations if M is projective, and so are abelian varieties, while the ones constructed by Griffiths behave well under . A complex structure on a real vector space is given by an automorphism I with square . The complex structures on are defined using the Hodge decomposition On the Weil complex structure is multiplication by , while the Griffiths complex structure is multiplication by if and if . Both these complex structures map into itself and so defined complex structures on it. For the intermediate Jacobian is the Picard variety, and for it is the Albanese variety. In these two extreme cases the constructions of Weil and Griffiths are equivalent. used intermediate Jacobians to show that non-singular cubic threefolds are not rational, even though they are unirational. (Wikipedia).
David Masser: Avoiding Jacobians
Abstract: It is classical that, for example, there is a simple abelian variety of dimension 4 which is not the jacobian of any curve of genus 4, and it is not hard to see that there is one defined over the field of all algebraic numbers \overline{\bf Q}. In 2012 Chai and Oort asked if ther
From playlist Algebraic and Complex Geometry
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From playlist Intermediate Algebra
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From playlist Multivariable calculus
Gentle example explaining how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations
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From playlist Solving Systems of Nonlinear Equations
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From playlist Intermediate Algebra (Full Length Videos)
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Normal functions and the geometry of moduli spaces of curves - Richard Hain
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From playlist Mathematics
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Stanford CS229: Machine Learning | Summer 2019 | Lecture 11 - Deep Learning - II
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3jpCT1d Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
This video explains how to calculator a Jacobian for a change of variables.
From playlist Applications of Double Integrals: Mass, Center of Mass, Jacobian
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From playlist Mathematics
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From playlist Algebraic and Complex Geometry
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From playlist Lecture Collection | Convolutional Neural Networks for Visual Recognition (Spring 2017)