6 papers
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 .
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 s…
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…
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…
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…