A Minimal Model Program for $\mathbb{Q}$-Gorenstein varieties

Boris Pasquier (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

The Minimal Model Program is constructed for projective varieties with at most $\mathbb{Q}$-factorial terminal singularities. Here, we adapt the definitions of divisorial contractions and flips to construct a Minimal Model Program for projective varieties with at most $\mathbb{Q}$-Gorenstein terminal singularities. This new construction can be naturally extended to klt pairs. In the family of $\mathbb{Q}$-Gorenstein spherical varieties, we answer positively to the questions of existence of flips and of finiteness of sequences of flips.

Mots clés: Minimal Model Program

Domaines: Géométrie algébrique [math.AG]

Boris Pasquier. A Minimal Model Program for $\mathbb{Q}$-Gorenstein varieties. 2014. ⟨hal-01011335v1⟩