Here is a brief summary taken from Wikipedia:
In the poem, a young messenger has been sent by a Count to see the Duke, who is seeking to marry the young daughter of the Count. The Duke elaborates on the whimsical, giddy nature of his late wife, which certainly displeased him. Thus, he,"gave commands; / Then all smiles stopped together," and the implication is that he killed her in an extremely jealous rage. He now keeps her painting hidden behind a curtain that only he is allowed to draw back so now she only smiles her smile for him. The Duke then begins to cordially discuss wedding arrangements with the messenger and then changes the subject to point out a brass statue of Neptune taming a seahorse.
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