School of Mathematics Colloquium

# Generalized Jacobian Conjecture

## by Prof. R.V. Gurjar (IIT, Mumbai)

Thursday, October 12, 2017 from to (Asia/Kolkata)
at TIFR, Mumbai ( AG-69 )
 Description Abstract: M. Miyanishi generelized the usual Jacobian Conjecture as follows. Generalized Jacobian Conjecture. Let V be a normal affine variety. Suppose f:V \to V is an unramified morphism. Then f is a proper morphism. After discussing some earlier positive results and some counterexamples to GJC we will outline the proof of the following result proved jointly with M. Miyanishi. Theorem. Let V be an irreducible normal affine surface. Assume that V has at least one singular point which is not a quotient singular point. Then any unramified self morphism is an isomorphism.