Capitalize "I" on the second to last line.  Also, consider adding some punctuation to the ends of the lines.  You have the period at the very end, but also consider putting a period or comma at the end of some of your other lines to complement the natural flow of the poem.  You misspelled 'unfruitful,' 'mortality,' and 'immortality.'  I also think "white as snow" is a little cliche; it's a vastly over-used comparison, so maybe you could find something from your greek characters' perspective that they are familiar with to compare the whiteness to.

In line three, how did the speaker grant "immortality"? The object of the poem apparently is not immortal, so what happened? I understand that you said the gift was "unfruitful," but as a reader I need a little more to fully understand your point.

You have some good details and images in the second half of the poem.

I don't really think the first line works. My "mortal love" might work better. I also am not sure about the word "case" in the fourth line. I'm not sure exactly what you mean. In the 7th row, do you mean "mortality" instead? Of course the I needs to be capitalized in the last line. Good job!