Aslanyan, V, Kirby, J and Mantova, V orcid.org/0000-0002-8454-7315 (2023) A geometric approach to some systems of exponential equations. International Mathematics Research Notices, 2023 (5). pp. 4046-4081. ISSN 1073-7928
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2022. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Nov 2021 10:29 |
Last Modified: | 30 May 2023 22:38 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imrn/rnab340 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180865 |