A geometric approach to some systems of exponential equations

Aslanyan, Vahagn, Kirby, Jonathan 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 (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	27 Nov 2021 01:48
Last Modified:	15 Jul 2025 20:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/82387
DOI:	10.1093/imrn/rnab340

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