About the dual Schanuel conjecture (Joint logic and number theory seminar)

Vincenzo Mantova (Leeds)

Frank Adams 1,

 Schanuel's conjecture predicts a lower bound for the transcendence

degree of the values of the complex exponential function. A lesser

known "dual" conjecture, formulated independently by Schanuel and by

Zilber, is the following: the graph of the exponential function must

intersect generically all "free rotund" algebraic varieties. This would

have strong consequences (i.e., quasi-minimality) for the model theory

of complex exponentiation.


I will discuss the recent positive results on this problem, which seems

to be tractable for curves and surfaces (including joint work in U.

Zannier and work in progress with D. Masser -- and provided one removes

or replaces the word "generically").

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