Pea comb/single comb is a single allele on chromosome 1. There are at least 2 other comb variants associated with this allele that I have seen. A chicken with 1 pea comb and one single comb gene will show a fat pea comb phenotype. Two copies of pea comb give a pure bred pea comb chicken. Two copies of single comb give a single comb with sexual dimorphism, meaning that roosters have a large single comb and hens have a small single comb.
Rose comb is from having two copies of single comb on chromosome 1 and two copies of the rose comb inversion on chromosome 7. There are several modifier genes associated with comb type so it is common to see birds with rose comb and "peaks". Having comb genes on different chromosomes explains why it is common for crosses involving rose comb to have a percentage of straight comb offspring.
All eggs start out white. This is inherited from theropod ancestors and is a result of calcium carbonate in the egg shell. This is the normal white eggs such as are common from red games and other breeds that lay a slightly cream colored egg. White egg is easily covered in a cross with a brown egg layer. There is a zinc white gene that makes the normal white eggs brighter. Mediterranean breeds such as Leghorns commonly have the zinc white gene. Zinc white will override the biopath for brown eggs to the point that the eggs have only a slight tan tint. Cross a Brown Leghorn (zinc white layer) with any brown egg layer and the F1's will all produce barely detectable tan tinted eggs.
The gene for blue eggs is on chromosome 1 (whether asian blue or south American blue) and is very close to the gene for straight/pea comb. It is closely enough linked that a homozygous blue egg layer with pea comb such as Ameraucanas and some easter eggers can be selected for the blue egg gene based on having pea comb. Blue egg is dominant meaning that if just 1 copy of the gene is present the hen will lay blue eggs. Blue egg and pea comb can be separated at a rate of roughly 1 in 35 F2 chicks. This is why there are so many straight comb blue egg layers today.
Porphyrin is the brown coating on eggs. Sometimes it is mixed in as the egg shell is formed producing stippled eggs. Porphyrin is NOT a gene. It is a "biopath" meaning that there are multiple genes involved in production of the brown egg coating. Here is where it gets tricky. All extant chickens have the porphyrin biopath, but in some breeds one or more genes disable it. Brown leghorns that lay such pretty white eggs do so because their porphyrin biopath is disabled! Some breeds have 2 genes that cause over-expression of the porphyrin biopath. These genes cause breeds such as Marans to produce very dark brown eggs.
What about green eggs? These are a result of a combination of chickens that do NOT have the zinc white gene, have the normal white egg gene, have the blue egg gene, and have the porphyrin biopath turned on. Combine this with the porphyrin over-expression genes and the result is commonly called an olive egger. I have not tried to separate out the genetic combination that causes spearmint green eggs, but it will involve a modified porphyrin biopath.
I've seen one example of an extremely blue egg posted on BYC. I would speculate that this is caused by over-expression of the oocyanin (blue egg) gene. It would be interesting to see if a breed could be developed that produced intensely blue eggs.