Shinnosuke Okawa
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Shinnosuke Okawa has a total of 34 co-authors. Here are the top co-authors by number of shared publications:
- Kazushi Ueda
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
12 shared publications - Daniel Chan
University of New South Wales, Sydney, Australia
4 shared publications - Makoto Miura
Korea Institute for Advanced Study, Seoul, Republic of Korea
4 shared publications - Colin Ingalls
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
3 shared publications - Tarig Abdelgadir
Loughborough University
3 shared publications - Andrea T. Ricolfi
Scuola Internazionale Superiore di Studi Avanzati SISSA and INFN Trieste Italy
2 shared publications
Latest Publications
- Open Access
Deformation theory for a morphism in the derived category with fixed lift of the codomain
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 categories. As an application, we give an alternative proof that semiorthogonal decompositions deform uniquely in smooth proper families of schemes.
Open AccessDeformation theory for a morphism in the derived category with fixed lift of the codomain
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 categories. As an application, we give an alternative proof that semiorthogonal decompositions deform uniquely in smooth proper families of schemes.
- Open Access
Marked Artin--Schelter surfaces of del Pezzo types
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 stacks of marked Artin--Schelter surfaces of del Pezzo types are birational to the moduli stacks of tuples consisting of a smooth projective curve of genus 1, two line bundles of degree 3, and a collection of line bundles of degree 1 on the curve.
Open AccessMarked Artin--Schelter surfaces of del Pezzo types
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 stacks of marked Artin--Schelter surfaces of del Pezzo types are birational to the moduli stacks of tuples consisting of a smooth projective curve of genus 1, two line bundles of degree 3, and a collection of line bundles of degree 1 on the curve.
- Open Access
- 15 July 2025
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 261, 1-19
DEGENERATIONS OF ORBIFOLD CURVES AS NONCOMMUTATIVE VARIETIES
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 degenerations of orbifold projective curves corresponding to collisions of stacky points from the point of view of noncommutative algebraic geometry.
- 15 July 2025
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 261, 1-19
Open AccessDEGENERATIONS OF ORBIFOLD CURVES AS NONCOMMUTATIVE VARIETIES
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 degenerations of orbifold projective curves corresponding to collisions of stacky points from the point of view of noncommutative algebraic geometry.
- 4 April 2025
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 378 (7) , 4509-4544
On stacky surfaces and noncommutative surfaces
Letbe an algebraically closed field of characteristic or zero. Let be a tame order of global dimension over a normal surface over such that is locally a direct summand of . We prove that there is a -gerbe over a smooth tame algebraic stack whose generic stabilizer is trivial, with coarse space such that the category of 1-twisted coherent sheaves on is equivalent to the category of coherent sheaves of modules on . Moreover, the stack is constructed explicitly through a sequence of root stacks, canonical stacks, and gerbes. This extends results of Reiten and Van den Bergh to finite characteristic and the global situation. As applications, in characteristic we prove that such orders are geometric noncommutative schemes in the sense of Orlov, and we study relations with Hochschild cohomology and Connes’ convolution algebra. - 4 April 2025
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 378 (7) , 4509-4544
On stacky surfaces and noncommutative surfaces
Letbe an algebraically closed field of characteristic or zero. Let be a tame order of global dimension over a normal surface over such that is locally a direct summand of . We prove that there is a -gerbe over a smooth tame algebraic stack whose generic stabilizer is trivial, with coarse space such that the category of 1-twisted coherent sheaves on is equivalent to the category of coherent sheaves of modules on . Moreover, the stack is constructed explicitly through a sequence of root stacks, canonical stacks, and gerbes. This extends results of Reiten and Van den Bergh to finite characteristic and the global situation. As applications, in characteristic we prove that such orders are geometric noncommutative schemes in the sense of Orlov, and we study relations with Hochschild cohomology and Connes’ convolution algebra. - Open Access
Compact moduli of marked noncommutative cubic surfaces
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 on a cubic surface. It is a toric variety containing the configuration space of six points on a plane in general position as a locally closed subvariety, and birationally parametrizes a class of AS-regular $\mathbb{Z}$-algebras.
Open AccessCompact moduli of marked noncommutative cubic surfaces
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 on a cubic surface. It is a toric variety containing the configuration space of six points on a plane in general position as a locally closed subvariety, and birationally parametrizes a class of AS-regular $\mathbb{Z}$-algebras.
- Open Access
On stacky surfaces and noncommutative surfaces
Let $\mathbf{k}$ be an algebraically closed field of characteristic $\geq 7$ or zero. Let $\mathcal{A}$ be a tame order of global dimension $2$ over a normal surface $X$ over $\mathbf{k}$ such that $\operatorname{Z}(\mathcal{A})=\mathcal{O}_{X}$ is locally a direct summand of $\mathcal{A}$. We prove that there is a $\mu_N$-gerbe $\mathcal{X}$ over a smooth tame algebraic stack whose generic stabilizer is trivial, with coarse space $X$ such that the category of 1-twisted coherent sheaves on $\mathcal{X}$ is equivalent to the category of coherent sheaves of modules on $\mathcal{A}$. Moreover, the stack $\mathcal{X}$ is constructed explicitly through a sequence of root stacks, canonical stacks, and gerbes. This extends results of Reiten and Van den Bergh to finite characteristic and the global situation. As applications, in characteristic $0$ we prove that such orders are geometric noncommutative schemes in the sense of Orlov, and we study relations with Hochschild cohomology and Connes' convolution algebra.Open AccessOn stacky surfaces and noncommutative surfaces
Let $\mathbf{k}$ be an algebraically closed field of characteristic $\geq 7$ or zero. Let $\mathcal{A}$ be a tame order of global dimension $2$ over a normal surface $X$ over $\mathbf{k}$ such that $\operatorname{Z}(\mathcal{A})=\mathcal{O}_{X}$ is locally a direct summand of $\mathcal{A}$. We prove that there is a $\mu_N$-gerbe $\mathcal{X}$ over a smooth tame algebraic stack whose generic stabilizer is trivial, with coarse space $X$ such that the category of 1-twisted coherent sheaves on $\mathcal{X}$ is equivalent to the category of coherent sheaves of modules on $\mathcal{A}$. Moreover, the stack $\mathcal{X}$ is constructed explicitly through a sequence of root stacks, canonical stacks, and gerbes. This extends results of Reiten and Van den Bergh to finite characteristic and the global situation. As applications, in characteristic $0$ we prove that such orders are geometric noncommutative schemes in the sense of Orlov, and we study relations with Hochschild cohomology and Connes' convolution algebra. - Open Access
A compact moduli of orbifold projective curves
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 pointed stable curves in the sense of Hassett with respect to the weights determined by the automorphism groups of the stacky points.
Open AccessA compact moduli of orbifold projective curves
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 pointed stable curves in the sense of Hassett with respect to the weights determined by the automorphism groups of the stacky points.
- Open Access
Semiorthogonal indecomposability of minimal irregular surfaces
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 canonical linear system. As an application we prove that the derived category of minimal surfaces $X$ with $H^1 (X,\mathcal{O}_X) \neq 0$ are semiorthogonally indecomposable.Open AccessSemiorthogonal indecomposability of minimal irregular surfaces
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 canonical linear system. As an application we prove that the derived category of minimal surfaces $X$ with $H^1 (X,\mathcal{O}_X) \neq 0$ are semiorthogonally indecomposable. - 8 March 2023
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 303 (4) , 1-29
The minimal model program for b-log canonical divisors and applications
- 8 March 2023
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 303 (4) , 1-29
The minimal model program for b-log canonical divisors and applications
- 3 October 2020
- Published by Springer Nature in manuscripta mathematica
- Vol. 166 (1-2) , 1-17
On ruled surfaces with big anti-canonical divisor and numerically trivial divisors on weak log Fano surfaces
- 3 October 2020
- Published by Springer Nature in manuscripta mathematica
- Vol. 166 (1-2) , 1-17
On ruled surfaces with big anti-canonical divisor and numerically trivial divisors on weak log Fano surfaces