  We prove that if Y is a hypersurface of degree d in P^n with isolated
singularities, then the log canonical threshold of (P^n,Y) is at least
min{n/d,1}. Moreover, if d is at least n+1, then we have equality if and only
if Y is the projective cone over a (smooth) hypersurface in P^{n-1}. In the
case when Y is a hyperplane section of a smooth hypersurface in P^{n+1},
Cheltsov and Park have proved that Y has isolated singularities and they have
obtained the above lower bound for the log canonical threshold. Moreover they
made the conjecture about the equality case (for d=n+1) and they proved that
the conjecture follows from the Log Minimal Model Program. The purpose of this
note is to give an easy proof of their conjecture using the description of the
log canonical threshold in terms of jet schemes.
