Values distribution of holomorphic curves on annuli into projective varieties with hypersurface targets

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.