• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Admissible subcategories of del Pezzo surfaces
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
August 25, 2026
Scientists Develop Algorithm for More Reliable Processors in Data Centres
Researchers from HSE MIEM and Samara University have developed the LRF-3D algorithm to automatically bypass idle nodes in three-dimensional networks-on-chip. Thanks to its hierarchical architecture, the algorithm outperforms existing solutions in both speed and path accuracy, improving processor reliability for use in data centres, supercomputers, and AI computing. The source code and test results are publicly available.
August 24, 2026
Researchers Develop Method for Direct Generation of Regulatory DNA
Researchers at HSE University have developed a model for generating promoters and enhancers—DNA sequences that regulate gene activity. The model works directly with DNA nucleotides, without first transforming them into a continuous numerical representation. This solution could be useful for applications in synthetic biology and gene therapy. The study results were presented at the ICLR 2026 Workshop ‘Generative AI in Genomics (Gen^2): Barriers and Frontiers.’
August 21, 2026
Social Integration: At the Crossroads of Knowledge and Values
The International Laboratory for Social Integration Research (ILSIR) at HSE University studies the challenges faced by vulnerable groups and explores ways to help them participate fully in everyday life. To develop effective solutions, the laboratory’s researchers combine cutting-edge methods with practical fieldwork. In this interview with the HSE News Service, Laboratory Head Elena Iarskaia-Smirnova discusses the laboratory’s work.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Admissible subcategories of del Pezzo surfaces

Advances in Mathematics. 2023. Vol. 424. Article 109046.
Pirozhkov Dmitrii

We study admissible subcategories of derived categories of coherent sheaves on del Pezzo surfaces and rational elliptic surfaces. Using a relation between admissible subcategories and anticanonical divisors we prove the following results. First, we classify all admissible subcategories of the projective plane by showing that each is generated by a subcollection of a full exceptional collection. Second, we show that the derived categories of del Pezzo surfaces do not contain any phantom subcategories. This provides first examples of varieties of dimension larger than one that have some nontrivial admissible subcategories, but provably do not contain phantoms. We also prove that any admissible subcategory supported set-theoretically on a smooth -curve in a surface is generated by some twist of the structure sheaf of that curve.

Language: English
DOI
Text on another site
Keywords: semiorthogonal decompositionsпроизводные категории когерентных пучковderived categories of coherent sheavesполуортогональные разложения
Similar publications
Rank Two Sheaves With Low Discriminant on the Fano Threefold of Index 2 and Degree 5
Vasilev D., / Series arXiv "math". 2025.
Added: October 14, 2025
Stably semiorthogonally indecomposable varieties
Pirozhkov Dmitrii, Épijournal de Géométrie Algébrique 2023 Vol. 7 Article 7700
A triangulated category is said to be indecomposable if it admits no nontrivial semiorthogonal decompositions. We introduce a definition of a noncommutatively stably semiorthogonally indecomposable (NSSI) variety. This propery implies, among other things, that each smooth proper subvariety has indecomposable derived category of coherent sheaves, and that if Y is NSSI, then for any variety ...
Added: September 29, 2023
Rouquier dimension of some blow-ups
Pirozhkov Dmitrii, European Journal of Mathematics 2023 Vol. 9 No. 2 Article 45
Raphaël Rouquier introduced an invariant of triangulated categories which is known as Rouquier dimension. Orlov conjectured that for any smooth quasi-projective variety X the Rouquier dimension of 𝐷bcoh(𝑋) is equal to dim𝑋. In this note we show that some blow-ups of projective spaces satisfy Orlov’s conjecture. This includes a blow-up of ℙ2 in nine arbitrary ...
Added: September 29, 2023
Semiorthogonal decompositions on total spaces of tautological bundles
Pirozhkov Dmitrii, International Mathematics Research Notices 2022 No. 3 P. 2250–2273
Let U be the tautological subbundle on the Grassmannian Gr(k,n)⁠. There is a natural morphism Tot(U)→An⁠. Using it, we give a semiorthogonal decomposition for the bounded derived category Dbcoh(Tot(U)) into several exceptional objects and several copies of Dbcoh(An)⁠. We also prove a global version of this result: given a vector bundle E with a regular ...
Added: September 29, 2023
Derived categories of singular surfaces
Shinder E., Kuznetsov A., Karmazyn J., Journal of the European Mathematical Society 2022 Vol. 24 No. 2 P. 461–526
We develop an approach that allows one to construct semiorthogonal decompositions of derived categories of surfaces with cyclic quotient singularities whose components are equivalent to derived categories of local finite-dimensional algebras. We first explain how to induce a semiorthogonal decomposition of a surface X with rational singularities from a semiorthogonal decomposition of its resolution. In the case when X ...
Added: November 24, 2022
Categorical measures for finite group actions
Bergh D., Gorchinskiy S., Larsen M. et al., Journal of Algebraic Geometry 2021 Vol. 30 P. 685–757
Given a variety with a finite group action, we compare its equivariant categorical measure, that is, the categorical measure of the corresponding quotient stack, and the categorical measure of the extended quotient. Using weak factorization for orbifolds, we show that for a wide range of cases that these two measures coincide. This implies, in particular, ...
Added: November 17, 2021
Graph potentials and moduli spaces of rank two bundles on a curve
Galkin S., Belmans P., Mukhopadhyay S., / Series math "arxiv.org". 2020. No. 2009.05568.
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode degenerations of the moduli space of rank 2 bundles with fixed determinant. We show that the birational type of the graph potential only depends on the homotopy type of ...
Added: April 15, 2021
Semiorthogonal decompositions on total spaces of tautological bundles
Pirozhkov D., / Series arXiv "math". 2018.
Let U be the tautological subbundle on the Grassmannian Gr(k,n). There is a natural morphism Tot(U)→𝔸^n. Using it, we give a semiorthogonal decomposition for the bounded derived category D^b_coh(Tot(U)) into several exceptional objects and several copies of D^b_coh(𝔸n). We also prove a global version of this result: given a vector bundle E with a regular section s, consider a subvariety of the ...
Added: December 6, 2018
Derived categories of Gushel-Mukai varieties
Kuznetsov A., Perry A., Compositio Mathematica 2018 Vol. 154 No. 7 P. 1362–1406
We study the derived categories of coherent sheaves on Gushel–Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety is even or odd. We analyze the basic properties of this category using Hochschild homology, ...
Added: September 13, 2018
On the bounded derived category of $\mathsf{IGr}(3, 7)$
Anton Fonarev, / Series arXiv "math". 2018.
We construct a mininal Lefschetz decomposition of the bounded derived category of coherent sheaves on the isotropic Grassmannian $\IGr(3,7)$. Moreover, we show that $\IGr(3, 7)$ admits a full exceptional collection consisting of equivariant vector bundles. ...
Added: April 20, 2018
Derived Categories of Curves as Components of Fano Manifolds
Fonarev A., Kuznetsov A., Journal of London Mathematical Society 2018 Vol. 97 No. 2 P. 24–46
We prove that the derived category D(C) of a generic curve of genus greater than one embeds into the derived category D(M) of the moduli space M of rank two stable bundles on C with fixed determinant of odd degree. ...
Added: November 7, 2017
Canonical tilting relative generators
Bodzenta A., Bondal A. I., / Series arXiv "math". 2017.
Given a relatively projective birational morphism f:X→Y of smooth algebraic spaces with dimension of fibers bounded by 1, we construct tilting relative (over Y) generators TX,f and SX,f in Db(X). We develop a piece of general theory of strict admissible lattice filtrations in triangulated categories and show that Db(X) has such a filtration L where ...
Added: August 28, 2017
Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups
Polishchuk A., van der Bergh M., Journal of the European Mathematical Society 2019 Vol. 21 No. 9 P. 2653–2749
We consider the derived category of coherent sheaves on a complex vector space equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl groups of type A, B, G_2, F_4, as well as the groups G(m,1,n), we construct a semiorthogonal decomposition of this category, indexed by the conjugacy ...
Added: August 22, 2017
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit