When using the multi-mapping APIs ensure you set the splitOn param if you have keys other than Id”, “splitOn

You need to include the column you’d want to split on in your select query. Yours just selects all the other properties – so Dapper doesn’t find a matching column to split the objects.

Your query should probably be something like that:

var query = @"SELECT AlbumId, Title, Price, AlbumArtUrl, GenreId, Name, Description , ArtistId, Name ......" etc

Sam wrote an excellent answer for multi mappings and the splitOn option:
https://stackoverflow.com/a/7478958/1028323

Edit: If your query is as mentioned above, you’ll have to split on GenreId and ArtistId.

 AlbumId, Title, Price, AlbumArtUrl | GenreId, Name, Description | ArtistId, Name

The pipes are for the start of a new POCO you’re trying to map. So the SplitOn parameters would be GenreId and ArtistId.

Edit2: The problem is your POCO Album. You specify ArtistId and GenreId as properties but they basically belong to their respective POCO's.

public class Album
    {
        public virtual int AlbumId { get; set; }
        public virtual string Title { get; set; }
        public virtual decimal Price { get; set; }
        public virtual string AlbumArtUrl { get; set; }
        public virtual Genre Genre { get; set; }
        public virtual Artist Artist { get; set; }
    }

and

var sql = @"SELECT AL.AlbumId
                 , AL.Title
                 , AL.Price
                 , AL.AlbumArtUrl
                 , GE.GenreId
                 , GE.Name
                 , GE.Description
                 , AR.ArtistId
                 , AR.Name 
            FROM Album AL 
      INNER JOIN Artist AR ON AR.ArtistId = AL.ArtistId 
      INNER JOIN Genre GE ON GE.GenreId = AL.GenreId";

using (var conn = connFactory.OpenConnection())
{
    var res = conn.Query<Album, Genre, Artist, Album>(sql, (album, genre, artist) =>
    {
        album.Genre = genre;
        album.Artist = artist;
        return album;
    }, splitOn: "GenreId,ArtistId");
}

should do the trick. You don’t need GenreId and ArtistId anyway because you have a reference to those objects in Albums.