TY - JOUR
T1 - Weakly-exceptional singularities in higher dimensions
AU - Cheltsov, Ivan
AU - Shramov, Constantin
N1 - Funding Information:
We proved both Theorems 1.16 and 1.17 while participating in the Research in Groups program in the Center of International Research in Mathematics (Trento, Italy). We finished this paper at the Institute for the Physics and Mathematics of the Universe (Tokyo, Japan). We are really grateful to CIRM and IPMU for the beautiful working conditions. Special thanks goes to Sergey Galkin for his warm and encouraging support during our stay at IPMU. The work was also supported by the grants NSF DMS-1001427, N.Sh.-4713.2010.1, RFFI 11-01-00336-a, RFFI 11-01-92613-KO-a, RFFI 08-01-00395-a, RFFI 11-01-00185-a, and by AG Laboratory GU-HSE, RF government grant 11 11.G34.31.0023.
PY - 2014/4/30
Y1 - 2014/4/30
N2 - We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being weakly-exceptional for sixdimensional quotient singularities. The proof is naturally linked to various classical geometrical constructions related to subvarieties of small degree in projective spaces, in particular Bordiga surfaces and Bordiga threefolds.
AB - We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being weakly-exceptional for sixdimensional quotient singularities. The proof is naturally linked to various classical geometrical constructions related to subvarieties of small degree in projective spaces, in particular Bordiga surfaces and Bordiga threefolds.
UR - http://www.scopus.com/inward/record.url?scp=84900789554&partnerID=8YFLogxK
U2 - 10.1515/crelle-2012-0063
DO - 10.1515/crelle-2012-0063
M3 - Article
AN - SCOPUS:84900789554
SN - 0075-4102
SP - 201
EP - 241
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 689
ER -