Mathematics – Algebraic Geometry
Scientific paper
2010-11-12
Mathematics
Algebraic Geometry
48 pages. v4: Appendix is new, plus several minor changes made throughout the paper following the referee's suggestions. Final
Scientific paper
We introduce a notion of volume of a normal isolated singularity that generalizes Wahl's characteristic number of surface singularities to arbitrary dimensions. We prove a basic monotonicity property of this volume under finite morphisms. We draw several consequences regarding the existence of non-invertible finite endomorphisms fixing an isolated singularity. Using a cone construction, we deduce that the anticanonical divisor of any smooth projective variety carrying a non-invertible polarized endomorphism is pseudoeffective. Our techniques build on Shokurov's b-divisors. We define the notion of nef Weil b-divisors, and of nef envelopes of b-divisors. We relate the latter to the pull-back of Weil divisors introduced by de Fernex and Hacon. Using the subadditivity theorem for multiplier ideals with respect to pairs recently obtained by Takagi, we carry over to the isolated singularity case the intersection theory of nef Weil b-divisors formerly developed by Boucksom, Favre, and Jonsson in the smooth case.
Boucksom Sébastien
Favre Charles
Fernex Tommaso de
No associations
LandOfFree
The volume of an isolated singularity 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 The volume of an isolated singularity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The volume of an isolated singularity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-203587