Will God curse the earth?
No, after the flood, God swore he'd never again curse the earth.
And the LORD smelled a sweet savour; and the LORD said in his heart, I will not again curse the ground any more for man's sake. Genesis 8:21
But later, he threatens to do it again.
Behold, the LORD maketh the earth empty, and maketh it waste, and turneth it upside down, and scattereth abroad the inhabitants thereof. The land shall be utterly emptied, and utterly spoiled: for the LORD hath spoken this word. The earth mourneth and fadeth away, the world languisheth and fadeth away ... Therefore hath the curse devoured the earth, and they that dwell therein are desolate: therefore the inhabitants of the earth are burned, and few men left. Isaiah 24:1-6