We prove a generalization of Orlov's projectivization formula for the derived category D coh
b (P (E)), where E does not need to be a vector bundle; Instead, E is a coherent sheaf which …

This paper studies the derived category of the Quot scheme of rank $ d $ locally free
quotients of a sheaf $\mathscr {G} $ of homological dimension $\le 1$ over a scheme $ X …

In this paper, we study the counterpart of Grothendieck's projectivization construction in the
context of derived algebraic geometry. Our main results are as follows: First, we define the …

We show that certain Fano eightfolds (obtained as hyperplane sections of an orthogonal
Grassmannian, and studied by Ito–Miura–Okawa–Ueda and by Fatighenti–Mongardi) have …

This paper establishes semiorthogonal decompositions for derived Grassmannians of
perfect complexes with Tor-amplitude in $[0, 1] $. This result verifies the author's Quot …

This paper develops two theories, the geometric theory of derived Grassmannians (and flag
schemes) and the algebraic theory of derived Schur (and Weyl) functors, and establishes …

For a complex manifold equipped with an anti-holomorphic involution, which is referred to as
a real variety, the Smith-Thom inequality states that the total $\mathbb {F} _2 $-Betti number …

Conjecturally, Fano varieties of K3 type admit a multiplicative Chow–Künneth
decomposition, in the sense of Shen–Vial. We prove this for many of the families of Fano …

A classical result of Bondal–Orlov states that a standard flip in birational geometry gives rise
to a fully faithful functor between derived categories of coherent sheaves. We complete their …

Abstract We consider the Pfaffian–Grassmannian equivalence from the motivic point of view.
The main result is that under certain numerical conditions, both sides of the equivalence are …