International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 49, Pages 3101-3113

Jumping deformations of complete toric varieties

Hiroshi Sato

Department of Mathematics, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

Received 30 December 2002

Copyright © 2003 Hiroshi Sato. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We construct one-parameter complex analytic families whose special fibers are complete toric varieties. Under appropriate assumptions, the general fibers of these families also become toric varieties, and the corresponding fans are explicitly described by the data of the fans associated to the special fibers. Using these families, we construct a deformation family for a certain toric weakened Fano 3-fold. Moreover, we obtain certain examples of toric weakened Fano 4-folds.