The research focused on certain types of mathematical shapes called projective varieties and their symmetrical transformations. The scientists discovered that these shapes have the most independent symmetrical changes when they resemble a specific kind of shape called a complex torus or a related shape type. This confirms a belief that existed before. Additionally, they expanded on an earlier publication by Zhang from 2010, even though they didn't use it in this study. This information helps us understand more about the kinds of symmetries different geometrical shapes can have.