  We present a theoretical study of CMB temperature peaks, including its effect
over the polarization field, and allowing nonzero eccentricity. The formalism
is developed in harmonic space and using the covariant derivative on the
sphere, which guarantees that the expressions obtained are completely valid at
large scales (i.e., no flat approximation). The expected patterns induced by
the peak, either in temperature or polarization, are calculated, as well as
their covariances. It is found that the eccentricity introduces a quadrupolar
dependence in the peak shape, which is proportional to a complex bias parameter
$b_\epsilon$, characterizing the peak asymmetry and orientation. In addition,
the one-point statistics of the variables defining the peak on the sphere is
reviewed, finding some differences with respect to the flat case for large
peaks. Finally, we present a mechanism to simulate constrained CMB maps with a
particular peak on the field, which is an interesting tool for analysing the
statistical properties of the peaks present in the data.
