By definition, a Spin\(^c\) structure on a \(4\)-manifold \(M\) consists of a pair \(S^\pm\) of complex \(2\)-dimensional bundles over \(M\) with a common determinant bundle \(L\) and a Clifford multiplication \(TM \times S^+ \to S^-\). Any nonvanishing section \(\psi\) of \(S^+\) naturally induces an almost complex structure on \(M\) via the bundle isomorphism \(TM \to S^-\) given by the multiplication \(v\to v\psi\). Given an almost complex structure \(J\), we may consider pseudoholomorphic or totally real immersions of two-dimensional surfaces \(\Sigma\) into \(M\). In the present article the authors show how to generalize a definition of such immersions for the case when a Spin\(^c\) manifold has a section \(\psi\) of \(S^+\) with only isolated zeroes. Such a section is considered up to a multiplication by nonvanishing functions and induces an almost complex structure on the complement of the zero set of \(\psi\) via a Clifford multiplication by \(\psi/|\psi|\). An immersion \(\Sigma\to M^4\) is called totally real or pseudoholomorphic if it is totally real or pseudoholomorphic away from zeroes of \(\psi\). The authors classify pseudoholomorphic curves in the quaternion projective line \(\mathbb{H}P^1 = S^4\) endowed with the natural Spin\(^c\) structure. [This is an announcement of a corrected reprint of the article reviewed in Zbl 1080.53057.]