The moduli space of cubic surfaces and its compactifications are classical and date back to the mid-nineteenth century. While recent progress has been made in describing compactifications of moduli spaces for fully marked cubic surfaces using Kollár-Shepherd-Barron-Alexeev (KSBA) stable pairs with uniform weights, this talk explores an extension into asymmetric weights.

In particular, we investigate the KSBA compactification of moduli spaces of cubic surfaces with a single marked line by considering an asymmetric weight on one line and a uniform weight on the remaining 26 lines. We provide an explicit wall-and-chamber decomposition of the weight domain, giving 20 distinct chambers. These chambers yield new KSBA coarse moduli spaces that reveal how interactions between the marked line and cubic surface singularities give new wall crossings. We also give explicit descriptions of these weighted stable pairs parameterized by the moduli spaces in each chamber.