Abstract:

In this talk, I will describe moduli spaces for sextic curves with fixed types of simple singularities. I will explain that such moduli spaces admit algebraic open embeddings into arithmetic quotients of type IV domains. I will also describe the identifications of GIT compactifications with the Looijenga compactifications. Furthermore, I will discuss the Picard lattices and the relations of orbifold structures on two sides of the period maps. This is based on joint work with Chenglong Yu and Zhiwei Zheng.