This links to the part of the 2003 Act that gives local authorities the power to vary discounts on classes of dwellings determined by the Secretary of State - to a minumum of 10% on dwellings for classes of dwellings defined by their "physical characteristics" and to a minimum of nil for classes of dwellings that are unoccupied. 

These are the basic powers used to set the discounts for second homes and unfurnished empties. 

There is also a power (s.76)  to reduce the tax for individual people or classes of people, including to reduce it to zero.