Boundedness of log terminal Fano pairs of bounded index

Abstract

We prove a conjecture of Batryev which states that the family of all Fano varieties with kawamata log terminal singularities and fixed index, forms a bounded family.

22 pages

Cited by in corpus (10)

• Boundedness of spherical Fano varieties
• Toward the second main theorem on complements: from local to global
• Boundedness of anti-canonical volumes of singular log Fano threefolds
• Almost del Pezzo manifolds
• Shokurov's Rational Connectedness Conjecture
• Bounding the volumes of singular Fano threefolds
• Pluricanonical maps for threefolds of general type
• On algebraic varieties with finite polyhedral Mori cone
• On the pluricanonical maps of varieties of intermediate Kodaira dimension
• Boundedness of log-pluricanonical maps for surfaces of log-general types in positive characteristic