The Morifan of the Dolgachev-Nikulin-Voisin family of degree 2
Every projective threefold admits a fan structure on its moving cone coming from Mori theory. In particular, there is such a fan on the Dolgachev-Nikulin-Voisin K3 mirror family of degree 2d. Its relevance comes from applications to toroidal compactifications of polarised K3 surfaces, as carried out by Gross, Hacking, Keel and Siebert, and the fact that it gives a combinatorial description of the boundary of the KSBA compactification of stable K3 pairs.
In this talk, I will explain the construction of Dolgachev-Nikulin-Voisin families and outline the calculation of the Morifan in degree 2. This is joint work with K.Hulek.