this != Class name
this keyworkd basycally its call the class itself (already on memory, this means already called "new ClassName" (if is not a static class)), just try put a field on the beggining of the class like "private int test = 0;" and you can see that can call "this.private" that is the same to call "private" (inside the class)
If you need pass the Persons well just do :
serializerToXml.Serialize(write, new Persons()); // this is useless in certain way if you don't have a constructor to add data to this class