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

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Abstract

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 paper, 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.

Original languageEnglish
Article number1850042
JournalInternational Journal of Mathematics
Volume29
Issue number6
DOIs
Publication statusPublished - Jun 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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