Algebraic flows on commutative complex Lie groups
Tien-Cuong Dinh
National University of Singapore, SingaporeDuc-Viet Vu
Universität Köln, Germany and Thang Long Institute of Math. and Appl. Sci., Hanoi, Vietnam
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Abstract
We recover results by Ullmo–Yafaev and Peterzil–Starchenko on the closure of the image of an algebraic variety in a compact complex torus. Our approach uses directed closed currents and allows us to extend the result for dimension 1 flows to the setting of commutative complex Lie groups which are not necessarily compact. A version of the classical Ax–Lindemann–Weierstrass theorem for commutative complex Lie groups is also given.
Cite this article
Tien-Cuong Dinh, Duc-Viet Vu, Algebraic flows on commutative complex Lie groups. Comment. Math. Helv. 95 (2020), no. 3, pp. 421–460
DOI 10.4171/CMH/492