Kappa Classes on the KSBA Space of Stable Toric Pairs

Abstract

We study kappa classes on the normalization of the main component of the Kollár--Shepherd-Barron--Alexeev(KSBA) moduli space of stable toric pairs. Using a toric model obtained by a lattice modification, we compute all kappa classes on the moduli space by giving a combinatorial formula for their intersection numbers with all torus-invariant cycles. In particular, we identify the first normalized kappa class with the GKZ polarization of the toric variety corresponding to the secondary polytope. For interval configurations, we also obtain a closed formula for all top intersection products of normalized kappa classes.