"Self-aggrandizing Duke murders or exiles insufficiently appreciative wife" That's the plot. The quotation comes from this analysis which is as good as any I can find on the web.
http://poemshape.wordpress.com/2011/04/04/the-annotated-my-last-duchess/
When Robert Browning was asked what the Duke meant by "I gave commands then all smiles stopped together" he replied, ""I meant that the commands were that she should be put to death . . . or he might have had her shut up i
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