DK conjecture for some K-inequivalences from Grassmannians

Abstract

The DK conjecture of Bondal-Orlov [1] and Kawamata [2] states that there should be an embedding of bounded derived categories for any K-inequivalence, which is proved to be true for the toroidal case ([3], [4], [5] and [6]). In this paper, we construct examples of non-toroidal K-inequivalences from Grassmannians inspired by [7], [8], [9] and [10], and we show that these K-inequivalences satisfy the DK conjecture.