What are the precursors of the major plant hormones (auxin, gibberellin, cytokinin, ethylene, and abscisic acid)? What are the major genes that control/interact with them?
The major precursor of Auxin is most likely the amino acid Tryptophan. However the tryptophan is possibly derived from the shikimic acid pathway. Numerous enzymes would be utilized for Auxin alone. the ultimate precurser depends on how far you want to follow the production back.
The most common precursor of Cytokinins is believed to be Adenosine it involves a number of other possible precursors.
The genes involved are numerous and probably far from being completely understood
The synthesis and genetic control of hormones is a large topic, with multiple books and papers worth of information. In concise lets say a multitude of pathways feed into the diverse hormonal biosynthesis. Most hormone synthesis is under transcriptional control due to interconnected signaling pathways like developmental stage, biotic and abiotic stresses etc. Moreover, other levels of control also exist like the classic case of cellular trafficking of transporter localizations leading to changes in auxin localization. So theres obviously a genetic component as well as other cellular components that researchers are trying to understand.
I highly suggest reading some annual reviews or other review of hormone biosynthesis if you are interested in knowing more