Contact resolutions of projectivised nilpotent orbit closures

Baohua Fu (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

The projectivised nilpotent orbit closure P(\bar{O}) carries a natural contact structure on its smooth part. A resolution X \to P(\bar{O}) is called contact if the contact structure on P(O) extends to a contact structure on X. It turns out that contact resolutions, crepant resolutions and minimal models of P(\bar{O}) are all the same. In this note, we determine when the projectivised nilpotent orbit closure admits a contact resolution, and in the case of existence, we study the birational geometry among different contact resolutions.

Domaines: Géométrie algébrique [math.AG]

Baohua Fu. Contact resolutions of projectivised nilpotent orbit closures. 2007. ⟨hal-00018557v2⟩