  The purpose of this paper has twofold. The first is to establish a
Cartan-Nochka theorem for holomorphic curves from annuli into projective
varieties intersecting hypersurfaces in subgeneral position with truncated
counting functions. The second is to give a second main theorem for such curves
with arbitrary families of hypersurfaces, where the truncation level of the
counting functions is explicitly estimated not depending on the number of
hypersurfaces. As an application, we give a uniqueness theorem for such curves
sharing a few hypersurfaces in a projective variety ignoring multiplicity. Our
results generalize and improve the recent previous results in this topic.
