I wouldn't use polident or any abrasive. Try several sprays of vinegar, or a cloth soaked in vinegar. Place around faucet, It could take several applications. My Mom thought her new sink/cabinet in the bathroom was defective....at least the porcelain bowl part of it. There was a discoloration only where the water must have dripped....the line went down to the hole in the sink.....I brushed my finger over it and thought, this isn't a flaw...went to her kitchen got a rag, soaked it with vinegar and placed it over the stain.....after only five minutes, I rubbed it off. It was mineral build up. I use vinegar at my house now, all the time for cleaning around faucets.