Bounding the volumes of singular Fano threefolds

2012/04/12 by Lai, Ching-Jui · 2 citations
#14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.2593

Abstract

Let (X,Δ) be an n-dimensional ε-klt log \QQ-Fano pair. We give an upper bound for the volume \rm Vol(-(K_X+Δ))=(-(K_X+Δ))ⁿ when n=2 or n=3 and X is \QQ-factorial of ρ(X)=1. This bound is essentially sharp for n=2. Existence of an upper bound for anticanonical volumes is related the Borisov-Alexeev-Borisov Conjecture which asserts boundedness of the set of ε-klt log \QQ-Fano varieties of a given dimension n.

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