D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133

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Russian Academy of Sciences. Izvestiya Mathematics, 1993, Volume 41, Issue 1, Pages 133–141
DOI: https://doi.org/10.1070/IM1993v041n01ABEH002182 (Mi im929)

This article is cited in 143 scientific papers (total in 143 papers)

Projective bundles, monoidal transformations, and derived categories of coherent sheaves

D. O. Orlov

English version PDF (540 kB) Citations (143) Russian version article

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DOI: https://doi.org/10.1070/IM1993v041n01ABEH002182

Abstract: This paper studies derived categories of coherent sheaves on varieties that are obtained by projectivization of vector bundles and by monoidal transformations. Conditions for the existence of complete exceptional sets in such categories are derived; they give new examples of varieties on which exceptional sets exist.

Received: 05.06.1991

Bibliographic databases:

Document Type: Article

UDC: 512.73

MSC: Primary 14F05; Secondary 14E15, 14M15

Language: English

Original paper language: Russian

Citation: D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141

Citation in format AMSBIB

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\paper Projective bundles, monoidal transformations, and derived categories of coherent sheaves

\jour Russian Acad. Sci. Izv. Math.

\yr 1993

\vol 41

\issue 1

\pages 133--141

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Linking options:

https://www.mathnet.ru/eng/im929

https://doi.org/10.1070/IM1993v041n01ABEH002182

https://www.mathnet.ru/eng/im/v56/i4/p852

This publication is cited in the following 143 articles:

Todor Milanov, Xiaokun Xia, “Reflection Vectors and Quantum Cohomology of Blowups”, SIGMA, 20 (2024), 029, 60 pp.
Hsin-Ku Chen, “Minimal resolutions of threefolds”, era, 32:5 (2024), 3635
Tomoki Yoshida, “Full exceptional collections of line bundles on the blow-up of ${\mathbb {P}}^{5}$ along Segre threefold”, manuscripta math., 2024
Jenia Tevelev, Sebastián Torres, “The BGMN conjecture via stable pairs”, Duke Math. J., 173:18 (2024)
Russian Math. Surveys, 79:5 (2024), 807–845
Dmitrii Pirozhkov, “Admissible subcategories of del Pezzo surfaces”, Adv. Math., 424 (2023), 109046
Saša Novaković, “ON NONEXISTENCE OF FULL EXCEPTIONAL COLLECTIONS ON SOME RELATIVE FLAGS”, Rocky Mountain J. Math., 53:6 (2023)
Laura Pertusi, Paolo Stellari, “Categorical Torelli theorems: results and open problems”, Rend. Circ. Mat. Palermo, II. Ser, 72:5 (2023), 2949
Špela Špenko, Michel Van den Bergh, “Comparing the Kirwan and noncommutative resolutions of quotient varieties”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2023
Laurent Côté, Yusuf Barış Kartal, “Categorical action filtrations via localization and the growth as a symplectic invariant”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2023
Dae-Won Lee, “Classification of full exceptional collections on smooth toric Fano varieties with Picard rank two”, Advances in Geometry, 23:1 (2023), 25
Noah Olander, “Ample line bundles and generation time”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2023
Fonarev A., “On the Bounded Derived Category of Igr(3,7)”, Transform. Groups, 27:1 (2022), 89–112
Gonzales R. Pech C. Perrin N. Samokhin A., “Geometry of Horospherical Varieties of Picard Rank One”, Int. Math. Res. Notices, 2022:12 (2022), 8916–9012
Nunez P., “A Note on Semiorthogonal Decompositions For Fano Fibrations”, Geod. Dedic., 216:2 (2022), 20
Benjamin Gammage, Ian Le, “Mirror Symmetry for Truncated Cluster Varieties”, SIGMA, 18 (2022), 055, 30 pp.
A. Hanlon, J. Hicks, “Aspects of functoriality in homological mirror symmetry for toric varieties”, Advances in Mathematics, 401 (2022), 108317
Pieter Belmans, Lie Fu, Theo Raedschelders, “Derived categories of flips and cubic hypersurfaces”, Proceedings of London Math Soc, 125:6 (2022), 1452
Xie F., “Derived Categories of Quintic Del Pezzo Fibrations”, Sel. Math.-New Ser., 27:1 (2021), 4
Bergh D. Gorchinskiy S. Larsen M. Lunts V., “Categorical Measures For Finite Group Actions”, J. Algebr. Geom., 30:4 (2021), 685–757

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Statistics & downloads:
Abstract page:	1891
Russian version PDF:	780
English version PDF:	141
References:	121
First page:	4

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