Roman Polanski’s next directing effort will be his biggest undertaking yet in terms of scale, subject and budget.“Pompeii” is a dramatic thriller set against the backdrop of Mt. Vesuvius just before and during its eruption. The budget is projected to be $130 million, the director said. It is based on the bestseller of the same name by “Fatherland” novelist Robert Harris, who is writing the script. Filming will begin in Italy this summer.