17 citations · 105 across the 28 of their papers we have counts for
30 papers
Deformation theory for a morphism in the derived category with fixed lift of the codomain
Pieter Belmans, Wendy Lowen, Shinnosuke Okawa +1
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian catego…
Marked Artin--Schelter surfaces of del Pezzo types
Shinnosuke Okawa, Kazushi Ueda
We introduce a class of noncommutative surfaces called Artin--Schelter surfaces of del Pezzo types, which contains del Pezzo surfaces as special cases. We show that the moduli stac…
Compact moduli of marked noncommutative cubic surfaces
Tarig Abdelgadir, Shinnosuke Okawa, Kazushi Ueda
We introduce a compact moduli scheme of marked noncommutative cubic surfaces as the GIT moduli scheme of relations of a quiver associated with a full strong exceptional collection…
A compact moduli of orbifold projective curves
Tarig Abdelgadir, Daniel Chan, Shinnosuke Okawa +1
We introduce the notion of stable orbifold projective curves, and show that the moduli stack of stable orbifold projective curves is isomorphic to the moduli stack of weighted poin…
Degenerations of orbifold curves as noncommutative varieties
Tarig Abdelgadir, Daniel Chan, Shinnosuke Okawa +1
Boundary points on the moduli space of pointed curves corresponding to collisions of marked points have modular interpretations as degenerate curves. In this paper, we study degene…
Semiorthogonal indecomposability of minimal irregular surfaces
Shinnosuke Okawa
We prove a relative version of the fact that semiorthogonal decompositions of the bounded derived category of coherent sheaves are strongly constrained by the base locus of the can…
On stacky surfaces and noncommutative surfaces
Eleonore Faber, Colin Ingalls, Shinnosuke Okawa +1
Let be an algebraically closed field of characteristic or zero. Let be a tame order of global dimension over a normal surface over $\mat…
Exceptional collections on
Akira Ishii, Shinnosuke Okawa, Hokuto Uehara
Structure theorems for exceptional objects and exceptional collections of the bounded derived category of coherent sheaves on del Pezzo surfaces are established by Kuleshov and Orl…
AS-regular algebras from acyclic spherical helices
Shinnosuke Okawa, Kazushi Ueda
We discuss a construction of AS-regular algebras from acyclic spherical helices, generalizing works of Bondal and Polishchuk [BP93] and Van den Bergh [VdB11].
Indecomposability of derived categories in families
Francesco Bastianelli, Pieter Belmans, Shinnosuke Okawa +1
Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to ind…
Moduli spaces of semiorthogonal decompositions in families
Pieter Belmans, Shinnosuke Okawa, Andrea T. Ricolfi
To a smooth and proper morphism with quasicompact semiseparated target we associate a sheaf in the étale topology, which takes an affine -scheme to the se…
Moduli of noncommutative Hirzebruch surfaces
Izuru Mori, Shinnosuke Okawa, Kazushi Ueda
We introduce three non-compact moduli stacks parametrizing noncommutative deformations of Hirzebruch surfaces; the first is the moduli stack of locally free sheaf bimodules of rank…
On ruled surfaces with big anti-canonical divisor and numerically trivial divisors on weak log Fano surfaces
Rikito Ohta, Shinnosuke Okawa
We investigate the structure of geometrically ruled surfaces whose anti-canonical class is big. As an application we show that the Picard group of a normal projective surface whose…
An example of birationally inequivalent projective symplectic varieties which are D-equivalent and L-equivalent
Shinnosuke Okawa
We give an example of a pair of projective symplectic varieties in arbitrarily large dimensions which are D-equivalent, L-equivalent, and birationally inequivalent.
The minimal model program for b-log canonical divisors and applications
Daniel Chan, Kenneth Chan, Louis de Thanhoffer de Völcsey +8
We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log va…
Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties
Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1
In this paper, we discuss the problem of whether the difference of the classes of a Fourier--Mukai pair of smooth projective varieties in the Grothendieck ring o…
The class of the affine line is a zero divisor in the Grothendieck ring: via -Grassmannians
Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1
Motivated by [Bor] and [Mar], we show the equality in the Grothendieck ring of varieties, where is a pair of Calabi-Yau 3…
Calabi--Yau complete intersections in exceptional Grassmannians
Atsushi Ito, Makoto Miura, Shinnosuke Okawa +1
We classify completely reducible equivariant vector bundles on Grassmannians of exceptional Lie groups which give Calabi--Yau 3-folds as complete intersections. In particular, we f…
Nonexistence of semiorthogonal decompositions and sections of the canonical bundle
Kotaro Kawatani, Shinnosuke Okawa
For any admissible subcategory of the bounded derived category of coherent sheaves on a smooth proper variety, we prove that sections of the canonical bundle impose a strong constr…
Surfaces of globally -regular type are of Fano type
Shinnosuke Okawa
We prove that a projective surface of globally -regular type defined over a field of characteristic zero is of Fano type.
Noncommutative rigidity of the moduli stack of stable pointed curves
Shinnosuke Okawa, Taro Sano
We prove that the second Hochschild cohomology group of the moduli stack of stable -pointed genus curves vanishes for all but finitely many .
Compact moduli of noncommutative projective planes
Tarig Abdelgadir, Shinnosuke Okawa, Kazushi Ueda
We introduce the notion of the moduli stack of relations of a quiver. When the quiver with relations is derived-equivalent to an algebraic variety, the corresponding compact moduli…
Exceptional sheaves on the Hirzebruch surface
Shinnosuke Okawa, Hokuto Uehara
We investigate exceptional sheaves on the Hirzebruch surface , as the first attempt toward the classification of exceptional objects on weak del Pezzo surfaces.
Noncommutative quadric surfaces and noncommutative conifolds
Shinnosuke Okawa, Kazushi Ueda
We introduce a compact moduli of noncommutative quadrics, and show that it is the weighted projective space of weight (2,4,4,6). We also introduce a compact moduli of potentials fo…