Moduli of log Calabi Yau pairs


I will discuss joint work with Kenny Ascher, Dori Bejleri, Harold Blum, Giovanni Inchiostro, Yuchen Liu, and Xiaowei Wang on construction of moduli stacks and moduli spaces of log Calabi Yau pairs that can be realized as slc log Fano pairs with complements. Unlike moduli of canonically polarized varieties (respectively, Fano varieties) in which the moduli stack of KSB stable (respectively, K semistable) objects is bounded for fixed volume, dimension, the objects here form unbounded families. Despite this unbounded behavior, in the case of plane curve pairs (P2, C), we construct a projective good moduli space parameterizing S-equivalence classes of these slc Fanos with complements.