Bounded Complements for Weak Fano Pairs with Alpha-invariants and Volumes Bounded Below

2020/02/23 by Chen, Weichung
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.09899

Abstract

We show that fixed dimensional klt weak Fano pairs with alpha-invariants and volumes bounded away from 0 and the coefficients of the boundaries belonging to a fixed DCC set S form a bounded family. Moreover, such pairs admit a strong ε-lc ℝ-complement for some fixed ε>0.

Related

• Boundedness of varieties of Fano type with alpha-invariants and volumes bounded below
• Boundedness of klt complements on Fano fibrations over surfaces
• Boundedness of complements for generalized pairs
• On existence of bounded relative-global complements for Fano fibrations
• Boundedness of (ε, n)-Complements for projective generalized pairs of Fano type