Title
Fano hypersurfaces in weighted projective 4-spaces
Abstract
We determine the full list of anticanonically embedded quasismooth Fano hypersurfaces in weighted projective 4-spaces. There are 48 infinite series and 4442 sporadic examples. In particular, the Reid-Fletcher list of 95 types of anticanonically embedded quasismooth terminal Fano threefolds in weighted projective di-spaces is complete. We also prove that many of these Fano hypersurfaces admit a Kahler-Einstein metric, and study the nonexistence of tigers on these Fano 3-folds. Finally, we prove that there are only finitely many families of quasismooth Calabi-Yau hypersurfaces in weighted projective spaces of any given dimension. This implies finiteness for various families of general type hypersurfaces.
Year
DOI
Venue
2001
10.1080/10586458.2001.10504438
EXPERIMENTAL MATHEMATICS
Keywords
Field
DocType
calabi yau,algebraic geometry,infinite series
Topology,Series (mathematics),Mathematical analysis,Fano plane,Mathematics,Projective space,Projective test
Journal
Volume
Issue
ISSN
10.0
1.0
1058-6458
Citations 
PageRank 
References 
3
0.72
0
Authors
2
Name
Order
Citations
PageRank
Jennifer M Johnson1172.17
János Kollár2535.41