TY - JOUR
T1 - Fano compactifications of contractible affine 3-folds with trivial log canonical divisors
AU - Nagaoka, Masaru
N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85047252390&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85047252390&partnerID=8YFLogxK
U2 - 10.1142/S0129167X18500428
DO - 10.1142/S0129167X18500428
M3 - Article
AN - SCOPUS:85047252390
VL - 29
JO - International Journal of Mathematics
JF - International Journal of Mathematics
SN - 0129-167X
IS - 6
M1 - 1850042
ER -