Mathematics – Algebraic Geometry
Scientific paper
2009-01-04
Mathematics
Algebraic Geometry
26 pages; v3: in view of counter-examples found by Burt Totaro, Conjecture 1.2 appearing in version 2 has now been removed. To
Scientific paper
This paper is devoted to the study of various aspects of deformations of log pairs, especially in connection to questions related to the invariance of singularities and log plurigenera. In particular, using recent results from the minimal model program, we obtain an extension theorem for adjoint divisors in the spirit of Siu and Kawamata and more recent works of Hacon and McKernan. Our main motivation however comes from the study of deformations of Fano varieties. Our first application regards the behavior of Mori chamber decompositions in families of Fano varieties: we prove that, in the case of mild singularities, such decomposition is rigid under deformation when the dimension is small. We then turn to analyze deformation properties of toric Fano varieties, and prove that every simplicial toric Fano variety with at most terminal singularities is rigid under deformations (and in particular is not smoothable, if singular).
Fernex Tommaso de
Hacon Christopher D.
No associations
LandOfFree
Deformations of canonical pairs and Fano varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Deformations of canonical pairs and Fano varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deformations of canonical pairs and Fano varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-456556