Proceedings of the Indian Academy of Sciences - Mathematical Sciences

, Volume 104, Issue 3, pp 515-542

First online:

Some remarks on the Jacobian question

  • Shreeram S AbhyankarAffiliated withMathematics Department, Purdue University
  • , Marius Van Der Put
  • , William Heinzer
  • , Avinash Sathaye

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This revised version of Abhyankar's old lecture notes contains the original proof of the Galois case of then-variable Jacobian problem. They also contain proofs for some cases of the 2-variable Jacobian, including the two characteristic pairs case. In addition, proofs of some of the well-known formulas enunciated by Abhyankar are actually written down. These include the Taylor Resultant Formula and the Semigroup Conductor formula for plane curves. The notes are also meant to provide inspiration for applying the expansion theoretic techniques to the Jacobian problem.


Plane curves Jacobian automorphism Newton-Puiseux expansion