Hi, I saw the phrase "Comórtas Amhrán Eoraifíse", can anyone confirm is it gramatically correct, why would the form used be "Amhrán" here? thanks...

This is the so-called "functional genitive": When two nouns in the genitive follow each other directly, the first appears in the nominative but lenited. Of course, if this word begins with a vowel, there's nothing to lenite.

Other examples: Ord Bhlaosc an Bháis "Orden des Totenkopfs" ("order [of] skull [of] the death"); Biúró Oideachas Sláinte "Health Education Bureau" (i.e. "bureau [of] education [of] health").

Comórtas Amhrán Eoraifíse is literally a "Eurovision competition of songs". Here, amhrán "of songs" is the genitive plural of amhrán "a song". The genitive singular of many nouns in Irish (especially m1 and some f2 nouns) is the same as the nominative singular.

Think of "shoe box" and "toy factory" in English. A "shoe box" holds more than one shoe (usually a pair) and a "toy factory" makes more than one toy. In English, this is actually attributive use of the noun, but it does show that a singular noun in English may hide a plural meaning.

When looking at or forming compounds in Irish, be careful not to put everything in the genitive singular. See if it makes sense translated the long way, i.e., "of a song" vs "of songs", "of/for a shoe" vs "of/for shoes", "of/for a toy" vs "of/for toys", etc.

I'll just add a little to Domhnall and Breandán's explanations both of which are accurate in their way. Breandán casts a light on the Tuiseal Ginideach iolra that I never heard before or thought of myself.

In Irish we speak of "lag-iolra agus tréan-iolra" weak plural and strong plural.

The weak plural is the one that reverts to the form of the nominative singular in the genitive plural.

A weak plural is any plural formed by "caolú" or caolú + e" or by adding ~a

Strong plurals are all the other ways of showing the plural in Irish ~í, ~anna, ~acha, ~ta, srl Some "eisceachtaí" exceptions break this rule. "Drámaíocht na Scol" for example instead of "Drámaíocht na Scoileanna"

Caolú:
cat - eireaball an chait -- sceabhaíl na gcat
éan - nead an éin -- ceol na n-éan
coileach - glao an choiligh -- troid na gcoileach

Caolú + e:
cailleach - teach na caillí (= igh + e = í) - comhthionól na gcailleach