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Nick L
Nick L
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You don't necessarily have another Mori contraction, the Kleiman-Mori cone might stray outside the half space $-K_{X}.C >0$$-K_{Z}.C >0$, so one cannot guarantee the existence of two distinct extremal rays. Sometimes you have it, for example if the blow-up is Fano, but not always.

You don't necessarily have another Mori contraction, the Kleiman-Mori cone might stray outside the half space $-K_{X}.C >0$, so one cannot guarantee the existence of two distinct extremal rays. Sometimes you have it, for example if the blow-up is Fano, but not always.

You don't necessarily have another Mori contraction, the Kleiman-Mori cone might stray outside the half space $-K_{Z}.C >0$, so one cannot guarantee the existence of two distinct extremal rays. Sometimes you have it, for example if the blow-up is Fano, but not always.

Source Link
Nick L
Nick L
  • 7k
  • 1
  • 15
  • 41

You don't necessarily have another Mori contraction, the Kleiman-Mori cone might stray outside the half space $-K_{X}.C >0$, so one cannot guarantee the existence of two distinct extremal rays. Sometimes you have it, for example if the blow-up is Fano, but not always.