Group law on the neutral component of the Jacobian of a real hyperelliptic curve having many real components. (Q1874528)

A theorem by \textit{J. Huisman} [Indag. Math., New Ser. 12, No. 1, 73--81 (2001; Zbl 1014.14027)] states that the real part of the neutral component of the Jacobian variety of a real curve of genus \(g\), with at least \(g\) real branches, is isomorphic, as a group, to the product of any \(g\) of its real branches. In the present paper the author gives an explicit geometric description of this group law in the of hyperelliptic curves. We note that a similar result for the case of real plane quartic was given by \textit{J. Huisman} [J. Théor. Nombres Bordx. 14, No. 1, 249--256 (2002; Zbl 1019.14014)].