It looks like White can improve his position with 1. Qg7+ Kd5 2. Qd7+ Ke5 (2…Kc5 3. c4#) 3. Q:c7+ but I’m not sure it’s enough to win. I presume that next on the agenda for White is 4. Qd6 (or if Black prevents it with 3… Kd5 4. Qd7+ Ke5 5. d4+ to force entry to d6) to protect the d-pawn and allow the c-pawn to march forward.
I think white wins by stealing the queen. Either the king is x-rayed on the 5th rank or the d-pawn checks the king taking him off the black queen which is then taken for a lowly pawn.
1.Qh8+
(1…Kd5 2.Qd8+ Kxc6 3.Qe8+ Kc5 4.d4+)
1…Kf4
2.Qh4+ Ke3
3.Qf2+ Kxd3
4.Qf1+
White wins
Qh8 ez win
It looks like White can improve his position with 1. Qg7+ Kd5 2. Qd7+ Ke5 (2…Kc5 3. c4#) 3. Q:c7+ but I’m not sure it’s enough to win. I presume that next on the agenda for White is 4. Qd6 (or if Black prevents it with 3… Kd5 4. Qd7+ Ke5 5. d4+ to force entry to d6) to protect the d-pawn and allow the c-pawn to march forward.
I think white wins by stealing the queen. Either the king is x-rayed on the 5th rank or the d-pawn checks the king taking him off the black queen which is then taken for a lowly pawn.
1.Qh8+ Kf4 (Kd6 2.Qd8+ Kc5 3.d4+) 2.Qh4+ Ke3 3.Qf2+ winning
I agree with Kevin–it’s a Queen theft (X-ray) in exchange for the battle for the pawn on c6.
Qe8 and wait
1. Qh8
1. -, Kf5? 2. Qh5+ +-
1. -, Kf4 2. Qh4+, Ke3 (Ke5/Kf5 3. Qh5+ +-) 3. Qf2+, Kxd3 4. Qd1+ +-
1. -, Kd5/Kd6 2. Qd8+, Kxc6 (Kc5 3. d4+, Kxc6 4. Qe8+ +- or Ke5 3. Qg5+ +-) 3. Qe8+, Kc5 4. d4+ +-
White wins the queen in all lines.
This queen is busy as a bee.
1. Qh8 wins.
1… Kd6 2. Qd8 Ke5 3. Qg5
1… Kd6 2. Qd8 Kxc6 3. Qe8 Kc5 4. d4
1… Kf4 2. Qh4 Ke3 3. Qf2 Kxd3 4. Qf1
1… Kd5 2. Qh5 Kxc6 3. Qe8
1… Kf5 2. Qh5
1. Qh8 wins
To complete the first answer,
1.Qh8+ Kd5
2.Qd8+ Kc5
3.d4+ Kxc6
4.Qe8+
(Sansom, Endgame Studies by Sansom, 1990, #139)