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.
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Tien-Cuong Dinh, Duc-Viet Vu, Algebraic flows on commutative complex Lie groups. Comment. Math. Helv. 95 (2020), no. 3, pp. 421–460DOI 10.4171/CMH/492