Zingiber

1. Amomum Roxb. and Zingiber Mill. are two well recognised genera with numerous species each.
2. Amomum Roxb. is conserved against over the earlier homonym  Amomum L., nom. rej. (and as such Amomum L. is not rejected against Zingiber Mill.).
The reason for this is that when Amomum L. was first described by Linnaeus in his Flora Zeylanica (1747) where he classified three species in the Monandria monogynia. Six years after the first description, Linnaeus (1753) added a fourth species. These species have all been transferred to other genera, namely Aframomum, Elettaria and Zingiber (Burtt and Smith 1972), and Amomum Roxb. has been conserved with Amomum subulatum Roxb. as its conserved type (McNeill et al., 2006, appendix III).
3. Zingiber Mill. conserved with this spelling against the original spelling “Zinziber”.
4. If your question was pertaining to why Amomum zingiber L. was ignored while accepting Zingiber officinale Roscoe, the reason is that Linnaeus had described this species under genus Amomum but latter transferred to
Zingiber, where binomial Zingiber zingiber (L.) H. Karst. turned out to be a tautonym and as such rejected. This appears closely similar to tomato case where similar case resulted in Lycopersicon esculentum Mill. was declared as Nom. Cons. but with species transferred back to Solanum old Linnaean name Solanum lycopersicum got reinstated.
I hope this should help.

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As per efi thread:
Curcuma: leaves less than ten, distichous, lower one sheathing, penninerved, petiole proper well developed, shorter than leaf sheath belonging to it.
Zingiber: leaves numerous, distichous, the lower one reduced and sheath like, pinnately nerved, petiole very short or absent.