Mostly the stories kept me engaged despite the impending doom. Well-drawn characters, and the interconnection of the stories was very well done, with the characters moving in and out of each others' stories naturally. As the stories progress, the time moves forward as well. As such, the first couple of stories, The Son and The Heiress, take place mostly before the eruption even begins, and are only tangentially connected to the eruption. The latter stories have their action more and more taking place during the eruption, and, well... it's kind of like watching the film Titanic; you know there is no way in which this can end well for all the parties involved, especially for those who chose to try and hide in the city rather than flee.
My favorite stories were the Senator, because I loved the back and forth between the two main characters, and the Heiress, because I liked Aemilia's voice, and her slow revelation about Sabinus being actually being a good guy who she might love; my least favorite story was the Soldier, just because I wasn't terribly engaged by the characters.