5 papers · 1 filter
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…
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…
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…
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…
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…