  We present a general theory of the corrections to the asymptotic behaviour of
the Renyi entropies which measure the entanglement of an interval A of length L
with the rest of an infinite one-dimensional system, in the case when this is
described by a conformal field theory of central charge c. These can be due to
bulk irrelevant operators of scaling dimension x>2, in which case the leading
corrections are of the expected form L^{-2(x-2)} for values of n close to 1.
However for n>x/(x-2) corrections of the form L^{2-x-x/n} and L^{-2x/n} arise
and dominate the conventional terms. We also point out that the last type of
corrections can also occur with x less than 2. They arise from relevant
operators induced by the conical space-time singularities necessary to describe
the reduced density matrix. These agree with recent analytic and numerical
results for quantum spin chains. We also compute the effect of marginally
irrelevant bulk operators, which give a correction (log L)^{-2}, with a
universal amplitude. We present analogous results for the case when the
interval lies at the end of a semi-infinite system.
