7 papers
Tensor-generating line bundles on toric varieties
Daigo Ito, Michael R. Zeng, Xiangru Zeng
A line bundle is -generating if its powers generate the derived category of perfect complexes. Refining the derived Nakai--Moishezon criterion of Ito--Olander, we characte…
Bondal--Orlov reconstruction for tame stacks with trivial generic stabilizer
Daigo Ito, Noah Olander
We generalize the Bondal--Orlov Reconstruction Theorem to smooth, proper, tame algebraic stacks with generically trivial stabilizer, whose canonical bundles are nowhere torsion: Th…
Geometric Construction of Quiver Tensor Products
Daigo Ito, John S. Nolan
By a classic theorem of Beilinson, the perfect derived category of projective space is equivalent to the category of derived representations of…
A derived category analogue of the Nakai--Moishezon criterion
Daigo Ito, Noah Olander
We give a complete characterization of the line bundles on a proper variety whose tensor powers generate the derived category, answering a 2010 question of Chris Brav. The conditio…
Polarizations on a triangulated category
Daigo Ito
In a recent collaboration, Hiroki Matsui and the author introduced a new proof of the reconstruction theorem of Bondal-Orlov and Ballard, using Matsui's construction of a ringed sp…
A new proof of the Bondal-Orlov reconstruction using Matsui spectra
Daigo Ito, Hiroki Matsui
In 2005, Balmer defined the ringed space for a given tensor triangulated category, while in 2023, the second author introduced the ringed…
Gluing of Fourier-Mukai partners in a triangular spectrum and birational geometry
Daigo Ito
Balmer defined the tensor triangulated spectrum of a tensor triangulated category and showed that for a variety $X…