Jack,

The consensus is, most folks think that you should leave the stem to die back naturally so that whatever nutrients were in the stem will go back to the bulb, but that said, I usually cut them about half way down. They look better that way and after a few weeks you can pull the rest of the stem out of its socket so to speak and the bulb will have naturally sealed off that conduit into the bulb so water won't get in especially if you have your bulb outside.

If you cut the stem off too close to the bulb it might not dry properly and rot and the part that is still sticking into the bulb may cause rot inside the bulb. Quite satisfying to pop the dead stem out and know that it is all sealed naturally inside the socket.

Just my opinion of course...

Donna

I also follow Donna's method, as I have too often had the large stem fall over onto other plants. So, cutting it half way down prevents that problem for me. And, like Donna said then you can just pull the rest of it off when it is ready.

Thank you both, I will leave the stem until it dies back. Jack

Here is the FAQ posting. It might be of help. (Green text is active link)