In some vertebrates, what role does the "Sonic hedgehog" gene play in embryonic development?

The "Sonic the Hedgehog" gene codes for the Sonic the Hedgehog protein that is essential for fetal brain development. The protein is widespread in the brain from the spinal cord development to having a role in setting up the two hemispheres of the brain. SHH protein also plays a role in eye development. So far researchers have found over 100 mutations in the gene with varying consequences on the fetus. Nonsyndromic holoprosencephaly is the most common result of gene mutation. Unfortunately, the outcome is the brain hemispheres do not form and severe defects can result.

https://medlineplus.gov/genetics/gene/shh/

https://medlineplus.gov/genetics/condition/nonsyndromic-holoprosencephaly/

The origin of the name is interesting. researchers discovered a gene that controls embryonic development which they represented with the shorthand symbol hh.

The hh loss of function mutant phenotype causes the embryos to be covered with denticles, i.e. small pointy projections resembling the spikes of a hedgehog. ... Two of these genes, desert hedgehog and Indian hedgehog, were named for species of hedgehogs, while sonic hedgehog was named after the video game character Sonic the Hedgehog.The gene was named by Robert Riddle, a postdoctoral fellow at the Tabin Lab, after his wife Betsy Wilder came home with a magazine containing an advert for the game Sonic the Hedgehog.

https://en.wikipedia.org/wiki/Sonic_hedgehog_protein#Discovery_and_naming