On singular Fano varieties with a divisor of Picard number one. (English) Zbl 1437.14026

Montero, Pedro

Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 19, No. 2, 567-600 (2019).

The author studies the geometry of mildly singular Fano varieties on which there is an effective prime divisor of Picard number one.
The author first gives a good overview about the Minimal Model Program and extremal contractions. Then he proves his results on the cases where the variety has Picard number three and two.
Afterwards, he addresses the case of toric varieties. Once again it is given a clear overview on the subject before the main results are proven. Finally he treats the lifting of extremal contractions to universal covering spaces in codimension 1.

Reviewer: Rick Rischter (Itajubá)

MSC:

14E30	Minimal model program (Mori theory, extremal rays)
14H30	Coverings of curves, fundamental group
14J45	Fano varieties
14M25	Toric varieties, Newton polyhedra, Okounkov bodies

Keywords:

minimal model program; Fano varieties; extremal contractions