Fourfolds of Weil type and the spinor map

Recent papers by Markman and O’Grady give, besides their main results on the Hodge conjecture hyperkähler varieties, surprising explicit descriptions of families abelian fourfolds Weil type with trivial discriminant. They also provide a new perspective well-known fact that these varieties are Kuga Satake for certain weight two structures rank six. In this paper we give pedestrian introduction to results. The spinor map, which is defined using half-spin representation SO(8), used intensively. For simplicity, use basic theory avoid triality.