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Aslanyan, Vahagn, Kirby, Jonathan 
ORCID: https://orcid.org/0000-0003-4031-9107 and Mantova, Vincenzo
(2023)
A geometric approach to some systems of exponential equations.
International Mathematics Research Notices, 2023 (5).
4046–4081.
ISSN 1073-7928
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Abstract
Zilber’s Exponential Algebraic Closedness conjecture (also known as Zilber’s Nullstellensatz) gives conditions under which a complex algebraic variety should intersect the graph of the exponential map of a semiabelian variety. We prove the special case of the conjecture where the variety has dominant projection to the domain of the exponential map, for abelian varieties and for algebraic tori. Furthermore, in the situation where the intersection is 0-dimensional, we exhibit structure in the intersection by parametrizing the sufficiently large points as the images of the period lattice under a (multivalued) analytic map. Our approach is complex geometric, in contrast to a real analytic proof given by Brownawell and Masser just for the case of algebraic tori.
| Item Type: | Article |
|---|---|
| Additional Information: | Funding information: This work was supported by the Engineering and Physical Sciences Research Council [EP/S017313/1 to V.A. and J.K., EP/T018461/1 to V.M.]. |
| Uncontrolled Keywords: | mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600 |
| Faculty \ School: | Faculty of Science > School of Mathematics |
| UEA Research Groups: | Faculty of Science > Research Groups > Logic |
| Related URLs: | |
| Depositing User: | LivePure Connector |
| Date Deposited: | 27 Nov 2021 01:48 |
| Last Modified: | 24 Apr 2023 13:30 |
| URI: | https://ueaeprints.uea.ac.uk/id/eprint/82387 |
| DOI: | 10.1093/imrn/rnab340 |
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