On the unipotence of autoequivalences of toric complete intersection Calabi–Yau categories

Abstract

Consider the derived category of coherent sheaves, D b (X), on a compact Calabi–Yau complete intersection X in a toric variety. The scope of this work is to establish the (quasi-)unipotence of a class of elements in the group of autoequivalences, Aut(D b (X)). This is achieved by associating singularity categories, modelled by matrix factorizations, to the toric data. Each of these triangulated categories is equivalent to the derived category of coherent sheaves on X. The idea is then that, although the singularity categories share the group of autoequivalences, on each category there are elements in Aut(D b (X)), whose (quasi-)unipotence relations are easier to see than on the other categories.