429 citations · 3.4k across the 37 of their papers we have counts for
39 papers
Non-commutative Fano varieties and three-dimensional minifolds
Konstantin Loginov, Dmitri Orlov
We introduce notions of non-commutative Fano varieties and non-commutative minifolds, and study the latter in dimension three. We prove that the Euler matrices of full exceptional…
Unirational del Pezzo surfaces of degree one
Ivan Cheltsov, Konstantin Loginov, Dmitri Orlov +1
We construct explicit unirational del Pezzo surfaces of degree with arithmetic Picard rank one over , , and . Moreover, we prove that e…
Smooth DG algebras and twisted tensor product
Dmitri Orlov
In this paper, twisted tensor product of DG algebras is studied and sufficient conditions for smoothness of such a product are given. It is shown that in the case of finite-dimensi…
Finite-dimensional differential graded algebras and their geometric realizations
Dmitri Orlov
We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the categ…
Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
Dmitri Orlov
The main purpose of this paper is to describe various phenomena and certain constructions arising in the process of studying derived noncommutative schemes. Derived noncommutative…
Equivariant exceptional collections on smooth toric stacks
Lev Borisov, Dmitri Orlov
We study the bounded derived categories of torus-equivariant coherent sheaves on smooth toric varieties and Deligne-Mumford stacks. We construct and describe full exceptional colle…