Non-algebraic examples of manifolds with the volume density property
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- by Alexandre Ramos-Peon PDF
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Abstract:
Some Stein manifolds (with a volume form) have a large group of (volume-preserving) automorphisms: this is formalized by the (volume) density property, which has remarkable consequences. Until now all known manifolds with the volume density property are algebraic, and the tools used to establish this property are algebraic in nature. In this note we adapt a known criterion to the holomorphic case, and give the first examples of non-algebraic manifolds with the volume density property: they arise as suspensions or pseudo-affine modifications over Stein manifolds satisfying some technical properties. As an application we show that there are such manifolds that are potential counterexamples to the Zariski Cancellation Problem, a variant of the Tóth-Varolin conjecture, and the problem of linearization of $\mathbb {C}^*$-actions on $\mathbb {C}^3$.References
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Additional Information
- Alexandre Ramos-Peon
- Affiliation: Mathematisches Institut, Universität Bern Sidlerstr. 5 3012 Bern, Switzerland
- Email: alexandre.ramos@math.unibe.ch
- Received by editor(s): March 3, 2016
- Received by editor(s) in revised form: August 4, 2016, and September 23, 2016
- Published electronically: March 23, 2017
- Additional Notes: The author was partially supported by Schweizerischer Nationalfonds Grant 153120
- Communicated by: Franc Forstneric
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3899-3914
- MSC (2010): Primary 32M17, 32H02; Secondary 32M25, 14R10
- DOI: https://doi.org/10.1090/proc/13565
- MathSciNet review: 3665042