On singular Fano varieties with a divisor of Picard number one

Abstract

In this paper we study the geometry of mildly singular Fano varieties on which there is an effective prime divisor of Picard number one. Afterwards, we address the case of toric varieties. Finally, we treat the lifting of extremal contractions to universal covering spaces in codimension 1.

35 pages. Final version: to appear in Annali della Scuola Normale Superiore, Classe di Scienze

References in corpus (4)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Gorenstein toric Fano varieties
• Classifying terminal weighted projective space
• Variétés projectives complexes dont l'éclatée en un point est de Fano