would aniticipate his every need and smile only at him resulted in him ordering her death, which could be regarded as an expression of his ultimate mastery over the poor last duchess. If we consider how this statue you refer to is described, we can see similar themes emerging:

Notice Neptune, though,

Taming a seahorse, thought a rarity...

The key word to focus on here is the way that Neptune is shown "taming" a seahorse. Clearly we could argue that the Duke identifies himself with this figure of Neptune, the Roman God of the sea, in the way that he seeks to bring others under his control and go through a process of "taming" them so that they realise his ulimate mastery and power over them. We can therefore argue that this reference to the statue is another calculated demonstration of the Duke's power and the kind of obedience he expects from any future wife.

The nonchalant way in which the Duke, as if giving a tour of an art museum, calls upon his guest to "notice" this statue underlines his arrogance and utter hypocrisy, given the summary he has just provided of his wife's life and capacity to smile upon everyone, as if they were all equally worthy. He has criticized his wife for being too quick to like others and too easily pleased. Particularly, he seems irked that she would thank everyone as if their gifts were equal to his gift—of a "nine-hundred-years-old name." The Duke expected her to feel gratitude to him for having married her; he wanted to have been singular in her affections. At the same time, however, she was not singular even as his wife—she is described by him as "my last Duchess"— nor is she even singular as a piece of art, now hidden behind a curtain and revealed to special guests. The Duke has transformed his wife into simply a stop on a tour. He now progresses to indicate another object d'art, oblivious to what this implies about how little he valued his wife.

We can also draw some inference from the fact that the Duke says that he and his guest should "go together down." It seems that his companion, disgusted by the Duke's behavior, has started to proceed away from him. The reference to the statue, then, serves to keep the other man there. The Duke is trying to assert his will over him, too.

Modeled after Alfonso II, the fifth and last Italian duke of the principality of Ferrera, which later became part of the Papal states, the proud, possessive, and selfish Duke of Ferrera is a great lover of art, a dilettante.  In Browning's dramatic monologue, the duke pulls a curtain to display a frescoe of his deceased wife.  Redefined as an art object by the duke, the life of the Duchess is discussed by the duke as though it were a composition of art:

The dropping of the daylight in the West,

The bough of cherries some officious fool

Broke in the orchard for her, the white mule

She rode with round the terrace--

So, when the duke points to the statue of Neptune as he and his guest descend the stairs, it is as though this arrogant dilettante draws his guest's attention to yet another work of art.  But, while the duchess is painted onto the wall, this new exhibit is a sculpture, and a concluding piece to the tour of the duke's objets d'art.