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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 740–757 (Mi izv1202)  

This article is cited in 19 scientific papers (total in 19 papers)

Exceptional bundles on surfaces with a moving anticanonical class

A. L. Gorodentsev

Abstract: The author studies the properties of exceptional coherent sheaves on algebraic surfaces $S$ with $\operatorname{dim}H^0(-\mathscr K_S)\geqslant2$ and describes a method for constructing infinite families of such sheaves, based on the technique developed here of reconstructions of the exceptional objects of a derived category.
Bibliography: 12 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 67–83

Bibliographic databases:

UDC: 513.6
MSC: Primary 14F05, 18F15, 55R10; Secondary 14J10, 55R65
Received: 20.07.1987

Citation: A. L. Gorodentsev, “Exceptional bundles on surfaces with a moving anticanonical class”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 740–757; Math. USSR-Izv., 33:1 (1989), 67–83

Citation in format AMSBIB
\by A.~L.~Gorodentsev
\paper Exceptional bundles on surfaces with a~moving anticanonical class
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 4
\pages 740--757
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 67--83

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    This publication is cited in the following articles:
    1. A. N. Rudakov, “Exceptional vector bundles on a quadric”, Math. USSR-Izv., 33:1 (1989), 115–138  mathnet  crossref  mathscinet  zmath
    2. A. N. Tyurin, “Symplectic structures on the varieties of moduli of vector bundles on algebraic surfaces with $p_g>0$”, Math. USSR-Izv., 33:1 (1989), 139–177  mathnet  crossref  mathscinet  zmath
    3. D. Yu. Nogin, “Spirals of period 4 and equations of Markov type”, Math. USSR-Izv., 37:1 (1991), 209–226  mathnet  crossref  mathscinet  zmath  adsnasa
    4. B. V. Karpov, “Semistable sheaves on a two-dimensional quadric, and Kronecker modules”, Russian Acad. Sci. Izv. Math., 40:1 (1993), 33–66  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. Yu. Ziuzina, “Constructibility of exceptional pairs of vector bundles on a quadric”, Russian Acad. Sci. Izv. Math., 42:1 (1994), 163–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. S. A. Kuleshov, D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 479–513  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Eric Zaslow, “Solitons and helices: The search for a math-physics bridge”, Comm Math Phys, 175:2 (1996), 337  crossref  mathscinet  zmath
    8. B. V. Karpov, D. Yu. Nogin, “Three-block exceptional collections over Del Pezzo surfaces”, Izv. Math., 62:3 (1998), 429–463  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. L. Gorodentsev, S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440  mathnet  crossref  mathscinet  zmath
    10. B. V. Karpov, “Monads of Stable Non-bundles on $\mathbb P^2$”, Proc. Steklov Inst. Math., 246 (2004), 142–145  mathnet  mathscinet  zmath
    11. Meltzer H., “Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines”, Mem. Am. Math. Soc., 171:808 (2004), III+  mathscinet  isi
    12. Aaron Bergman, “Undoing orbifold quivers”, J High Energy Phys, 2007:3 (2007), 112  crossref  mathscinet
    13. L. COSTA, R. M. MIRÓ–ROIG, “Geometric collections and Castelnuovo–Mumford regularity”, Math Proc Camb Phil Soc, 143:3 (2007)  crossref  zmath  isi
    14. Miro-Roig, RM, “Cohomological characterisation of Steiner bundles”, Forum Mathematicum, 21:5 (2009), 871  crossref  isi
    15. Lutz Hille, Markus Perling, “Exceptional sequences of invertible sheaves on rational surfaces”, Compositio Math, 2011, 1  crossref
    16. Okawa Sh. Uehara H., “Exceptional Sheaves on the Hirzebruch Surface _{2}”, Int. Math. Res. Notices, 2015, no. 23, 12781–12803  crossref  mathscinet  zmath  isi  scopus
    17. Chunyi Li, “Deformations of the Hilbert scheme of points on a del Pezzo surface”, Mosc. Math. J., 17:2 (2017), 291–321  mathnet  crossref  mathscinet
    18. Auel A. Bernardara M., “Cycles, Derived Categories, and Rationality”, Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 95, ed. Coskun I. DeFernex T. Gibney A., Amer Mathematical Soc, 2017, 199–266  crossref  isi
    19. Auel A., Bernardara M., “Semiorthogonal Decompositions and Birational Geometry of Del Pezzo Surfaces Over Arbitrary Fields”, Proc. London Math. Soc., 117:1 (2018), 1–64  crossref  isi
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