Any process that activates, maintains or increases the frequency, rate or extent of phytoalexin biosynthesis, the chemical reactions and pathways resulting in the formation of phytoalexins.
Synonyms:
exact_synonym:
positive regulation of phytoalexin biosynthesis; up regulation of phytoalexin biosynthesis; upregulation of phytoalexin biosynthesis
narrow_synonym:
activation of phytoalexin biosynthesis; stimulation of phytoalexin biosynthesis