We prove a Knörrer-periodicity-type equivalence between derived factorization categories of
gauged Landau–Ginzburg models, which is an analogy of a theorem proved by Shipman …

We study the birational properties of geometrically rational surfaces from a derived
categorical perspective. In particular, we give a criterion for the rationality of a del Pezzo …

We discuss recent developments in the study of semiorthogonal decompositions of
algebraic varieties with an emphasis on their behaviour in families. First, we overview new …

Given a gauged linear sigma model (GLSM) TX realizing a projective variety X in one of its
phases, ie its quantum Kähler moduli has a geometric point, we propose an extended GLSM …

We study hybrid models arising as homological projective duals (HPD) of certain projective
embeddings f: X→ P (V) of Fano manifolds X. More precisely, the category of B-branes of …

Kuznetsov's homological projective duality (HPD) theory [K4] is one of the most active and
powerful recent developments in the homological study of algebraic geometry. The …

Our main goal is to give a sense of recent developments in the (stable) rationality problem
from the point of view of unramified cohomology and 0-cycles as well as derived categories …

We first prove semi‐orthogonal decompositions of derived factorization categories arising
from sums of potentials of gauged Landau–Ginzburg models, where the sums are not …

We prove that the derived category of a smooth complete intersection variety is equivalent to
a full subcategory of the derived category of a smooth projective Fano variety. This enables …

We study the derived category of a complete intersection into a derived category of
factorisations on a Landau–Ginzburg (LG) model, and then apply VGIT to obtain a birational …