Constructing curves with high rank via symmetry

For any g > 1, we construct a curve of genus g defined over the rational function field of many variables Q(t₁, . . . , t_N), with rank at least 4g + 7. An immediate consequence is that there exists an infinite family of (nonconstant) curves of genus g over Q with rank at least 4g + 7, which will improve the bound 3g + 7 which Néron claimed in 1954.