37 citations · 51 across the 7 of their papers we have counts for
12 papers
A categorical Torelli theorem for quartic del Pezzo surfaces
Alexey Elagin
We solve categorical Torelli problem for quartic del Pezzo surfaces. That is, we prove that a del Pezzo surface of degree can be canonically reconstructed from its Kuznetsov co…
On cyclic strong exceptional collections of line bundles on surfaces
Alexey Elagin, Junyan Xu, Shizhuo Zhang
We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation i…
Thick subcategories on curves
Alexey Elagin, Valery A. Lunts
We classify thick subcategories for smooth projective curves over an algebraically closed field.
Calculating dimension of triangulated categories: path algebras, their tensor powers and orbifold projective lines
Alexey Elagin
This is a companion paper of arXiv:1901.09461, where different notions of dimension for triangulated categories are discussed. Here we compute dimensions for some examples of trian…
Derived categories of coherent sheaves on some zero-dimensional schemes
Alexey Elagin, Valery A. Lunts
Let be the second infinitesimal neighborhood of a closed point in -dimensional affine space. In this note we study , the bounded derived category of cohere…
Three notions of dimension for triangulated categories
Alexey Elagin, Valery A. Lunts
In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these…
Smoothness of Derived Categories of Algebras
Alexey Elagin, Valery A. Lunts, Olaf M. Schnürer
We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a quest…
Regular subcategories in bounded derived categories of affine schemes
Alexey Elagin, Valery Lunts
Let be a commutative Noetherian ring such that is connected. We prove that the category contains no proper full triangulated subcategories which are reg…
On exceptional collections of line bundles on weak del Pezzo surfaces
Alexey Elagin, Junyan Xu, Shizhuo Zhang
We study full exceptional collections of line bundles on surfaces. We prove that any full strong exceptional collection of line bundles on a weak del Pezzo surface of degree $\ge 3…
A criterion for left-orthogonality of an effective divisor on a surface
Alexey Elagin
We find a criterion for an effective divisor on a smooth surface to be left-orthogonal or strongly left-orthogonal (i.e. for the pair of line bundles $(\mathcal O,\mathcal O(D)…
On full exceptional collections of line bundles on del Pezzo surfaces
Alexey Elagin, Valery Lunts
We prove that any numerically exceptional collection of maximal length, consisting of line bundles, on a smooth del Pezzo surface is a standard augmentation in the sense of L.Hille…
On equivariant triangulated categories
Alexey Elagin
Consider a finite group acting on a triangulated category . In this paper we investigate triangulated structure on the category of -equivariant ob…