Nice quick mate!
very nice checkmate
although I think 13... Bd6 14Qd2 loses to Nd5 and 13...Bd6 14Qe4 has to deal with e5
You're right, Kh7 in response to Qd2 is good. But in response to 14. Qe3 Kh7, there is 15. Qe4+ Kg8 16. Qg4+ with unavoidable mate.
I'm not certain the combination leads to mate by force: 13...Bd6 14.Qd2?! Nd7 and the obvious continuation 15. Qxh6 Nxf6 16Qxf6 doesn't seem to lead to mate. (Qe3 fares no better against Nd7). I still like white here, he has an h-pawn to push or perhaps a rook lift to finish black off, but I think black is clinging stubbornly to life... if Black has to give back his extra piece to survive he'll be going into the ending two pawns down though... still, I dunno, there may have been a bit of game left against best defense by black.
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Did I miss something? Anybody see a forcing line to mate? I see a line forcing to perpetual, but I think white wants more than a draw ;)