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Oct 26, 2010 at 0:31 comment added Allen Knutson I prefer to think of the map in the variant as $\det: M_{2\times 2} \to {\mathbb A}^1$.
Oct 25, 2010 at 21:22 vote accept Ben Webster
Oct 25, 2010 at 21:19 comment added Angelo Dear Ben, I believe that the modified version above should satisfy your conditions.
Oct 25, 2010 at 21:15 history edited Angelo CC BY-SA 2.5
added 205 characters in body; edited body
Oct 25, 2010 at 19:34 comment added Ben Webster While this is an interesting example, it doesn't actually answer my question; the fiber at the origin doesn't have rational singularities, since its normalization is disconnected.
Oct 25, 2010 at 16:09 comment added Angelo To Allen: nice statement, though!
Oct 25, 2010 at 14:30 comment added Allen Knutson I had the exact same counterexample typed up and was about to submit! The only remaining value added was the statement "Degeneration can produce new fixed points."
Oct 25, 2010 at 14:25 history answered Angelo CC BY-SA 2.5