Fano compactifications of contractible affine 3-folds with trivial log canonical divisors

2017/08/09 by Masaru Nagaoka, Nagaoka, Masaru
Mathematics · #14J30 #14J45 #14R10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J30 #msc:14J45 #msc:14R10

paper · pdf · doi:10.48550/arxiv.1708.02713

29 pages

arxiv created 2017/08/09 · arxiv updated 2017/08/10

Abstract

T.Kishimoto raised the problem to classify all compactifications of contractible affine 3-folds into smooth Fano 3-folds with second Betti number two and classified such compactifications whose log canonical divisors are not nef. In this article, we show that there are 14 deformation equivalence classes of smooth Fano 3-folds which can admit structures of such compactifications whose log canonical divisors are trivial. We also construct an example of such compactifications with trivial log canonical divisors for each of all the 14 classes.

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