Deformation types of Looijenga pairs of small length

Abstract

Following the work already done by E. Looijenga and others, we provide an analysis of the deformation types of Looijenga (or anticanonical) pairs $(Y,D)$, where the anticanonical divisor $D$ is made of $n$ irreducible components and $6\leq n \leq9$. In doing so we also give a description of their toric models.