DK Conjecture for Some $K$-inequivalences from Grassmannians

TL;DR

This paper constructs examples of non-toroidal K-inequivalences from Grassmannians and demonstrates that these satisfy the DK conjecture, expanding the understanding of derived category embeddings in algebraic geometry.

Contribution

It provides new explicit examples of non-toroidal K-inequivalences from Grassmannians that verify the DK conjecture, previously known mainly for toroidal cases.

Findings

Constructed non-toroidal K-inequivalences from Grassmannians.

Verified these K-inequivalences satisfy the DK conjecture.

Extended the class of known cases where the DK conjecture holds.

Abstract

The DK conjecture of Bondal-Orlov and Kawamata 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. In this paper, we construct examples of non-toroidal $K$-inequivalences from Grassmannians inspired by Kuznetsov, Kanemitsu, Ueda, and Morimura, and we show that these $K$-inequivalences satisfy the DK conjecture.