Timeline for Is an algebraic bijection from a projective variety to itself necessarily an isomorphism?
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| Mar 3, 2010 at 14:16 | comment | added | damiano | I have looked at the argument in Kaliman's paper and indeed it is very similar to the one given below. The reason for which Kaliman needs irreducible varieties is that he is interested in showing something different. The example on the first page of Kaliman's paper is exactly the main issue: he wants to be able to forget codimension two subschemes and still retain enough information. In particular, he cannot distinguish a scheme that becomes disconnected by removing a codimension two subscheme from its normalization. | |
| Mar 2, 2010 at 20:38 | comment | added | Peter Tingley | Yes, not requiring irreducibility is important. Frank's argument seems to be more or less the same as the one in Kaliman's paper, but perhaps you are right that their varieties are irreducible.. | |
| Mar 2, 2010 at 18:56 | history | answered | damiano | CC BY-SA 2.5 |