“…For example, the conjecture holds for dim 𝑋 = 1. The Cartan's second main theorem, where 𝑋 = ℙ 𝑛 and 𝐷 = 𝐻 1 + ⋯ + 𝐻 𝑞 , where the 𝐻 𝑖 are hyperplanes in general position, suggests that (1.1) holds with 𝑁 (1) 𝑓 (𝐷, 𝑟) replaced by ∑ 𝑞 𝑖=1 𝑁 (𝑛) 𝑓 (𝐻 𝑖 , 𝑟) under a weaker assumption that the map 𝑓 is linearly nondegenerate. When 𝑋 is a semiabelian variety, Noguchi, Winkleman and Yamanoi in [14] showed that the inequality (1.1) holds with 𝑁 (1) 𝑓 (𝐷, 𝑟) replaced by 𝑁 (𝑘 0 ) 𝑓 (𝐷, 𝑟) for some positive integer 𝑘 0 , and (1.2) holds if the map is algebraically nondegenerate.…”