Oil fell on Thursday on a surprise build in U.S. inventory levels and a firm dollar, but a recovery in Asian shares after Wall Street posted a near 2 percent gain checked losses. Asian investors were focused on the increase in U.S. crude inventories last week, but sentiment had been supported by the rally on Wall Street, said Jonathan Barratt, chief investment officer at Sydney’s Ayers Alliance. U.S. crude fell 19 cents to $46.06 a barrel, off the day’s low of $45.65, after settling up 84 cents on Wednesday.