Operations on -structures and perverse coherent sheaves

Abstract

We introduce the notions of consistent pairs and consistent chains of -structures and prove that two consistent chains of -structures generate a distributive lattice. The technique developed is then applied to the pairs of chains obtained from the standard -structure on the derived category of coherent sheaves and the dual -structure by means of the shift functor. This yields a family of -structures whose hearts are known as perverse coherent sheaves.