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 …

We show that for many moduli spaces of torsion sheaves on K3 surfaces, the functor
induced by the universal sheaf is a-functor, hence can be used to construct an …

Balmer defined the tensor triangulated spectrum $\operatorname {Spec} _\otimes\mathcal
{T} $ of a tensor triangulated category $(\mathcal {T},\otimes) $ and showed that for a variety …

For a cyclic group G acting on a smooth variety X with only one character occurring in the G-
equivariant decomposition of the normal bundle of the fixed point locus, we study the …

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 …

We give a new proof of the derived equivalence of a pair of varieties connected by the flop of
type C 2 in the list of Kanemitsu (2018), which is originally due to Segal (Bull. Lond. Math …

We use Picard-Lefschetz theory to introduce a new local model for the planar projective
twists $\tau_ {\mathbb {A}\mathbb {P}^ 2}\in\mathrm {Symp} _ {ct}(T^*\mathbb {A}\mathbb …

We consider certain universal functors on symmetric quotient stacks of Abelian varieties. In
dimension two, we discover a family of P-functors which induce new derived …

Flops are birational transformations which, conjecturally, induce derived equivalences. In
many cases an equivalence can be produced as pull-push via a resolution of the birational …