public
is an access modifier. Access modifiers specify from where you can access something and so are only valid on types or members. Your variable is a local, i.e. declared inside a method. Anything declared inside a method is only accessible to code inside that method so access modifiers would be meaningless.
In the case of types, e.g. classes and structures, the public
access modifier means that the type is accessible to code outside the assembly it is declared in. In the case of members, e.g. methods and properties, public
means that the member is accessible outside the type it is declared in. By that logic, public
on a local variable would mean accessible outside the method it's declared in, which is not possible and thus nonsensical and thus not allowed. Local variables are always effectively private
, i.e. accessible to code only at the same scope, and so no access modifier is required or allowed.