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Izv. Akad. Nauk SSSR Ser. Mat., 1988, Volume 52, Issue 4, Pages 788–812 (Mi izv1205)  

This article is cited in 17 scientific papers (total in 17 papers)

Exceptional vector bundles on a quadric

A. N. Rudakov


Abstract: This paper investigates exceptional vector bundles on a two-dimensional quadric. The method of helixes is used to show that any exceptional bundle and any helix are obtained by reconstruction of a helix of one-dimensional bundles.
Bibliography: 8 titles.

Full text: PDF file (3264 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1989, 33:1, 115–138

Bibliographic databases:

UDC: 513.6
MSC: Primary 14F05, 14J26; Secondary 18F20
Received: 06.07.1987

Citation: A. N. Rudakov, “Exceptional vector bundles on a quadric”, Izv. Akad. Nauk SSSR Ser. Mat., 52:4 (1988), 788–812; Math. USSR-Izv., 33:1 (1989), 115–138

Citation in format AMSBIB
\Bibitem{Rud88}
\by A.~N.~Rudakov
\paper Exceptional vector bundles on a~quadric
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1988
\vol 52
\issue 4
\pages 788--812
\mathnet{http://mi.mathnet.ru/izv1205}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=966985}
\zmath{https://zbmath.org/?q=an:0708.14012|0661.14015}
\transl
\jour Math. USSR-Izv.
\yr 1989
\vol 33
\issue 1
\pages 115--138
\crossref{https://doi.org/10.1070/IM1989v033n01ABEH000817}


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

    This publication is cited in the following articles:
    1. A. L. Gorodentsev, “Exceptional bundles on surfaces with a moving anticanonical class”, Math. USSR-Izv., 33:1 (1989), 67–83  mathnet  crossref  mathscinet  zmath
    2. A. I. Bondal, “Representation of associative algebras and coherent sheaves”, Math. USSR-Izv., 34:1 (1990), 23–42  mathnet  crossref  mathscinet  zmath
    3. S. A. Kuleshov, “An existence theorem for exceptional bundles on $\mathrm K3$ surfaces”, Math. USSR-Izv., 34:2 (1990), 373–388  mathnet  crossref  mathscinet  zmath
    4. 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
    5. D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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
    7. A. I. Bondal, A. E. Polishchuk, “Homological properties of associative algebras: the method of helices”, Russian Acad. Sci. Izv. Math., 42:2 (1994), 219–260  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. 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
    9. 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
    10. S. A. Kuleshov, “On moduli spaces for stable bundles on quadrics”, Math. Notes, 62:6 (1997), 707–725  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. 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
    12. A. L. Gorodentsev, S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440  mathnet  crossref  mathscinet  zmath
    13. Meltzer H., “Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines”, Mem. Am. Math. Soc., 171:808 (2004), III+  mathscinet  isi
    14. Bridgeland T., “T-structures on some local Calabi-Yau varieties”, Journal of Algebra, 289:2 (2005), 453–483  crossref  isi
    15. L. COSTA, R. M. MIRÓ–ROIG, “Geometric collections and Castelnuovo–Mumford regularity”, Math Proc Camb Phil Soc, 143:3 (2007)  crossref  zmath  isi
    16. 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
    17. V. M. Buchstaber, A. P. Veselov, “Conway topograph, $\mathrm{PGL}_2(\pmb{\mathbb Z})$-dynamics and two-valued groups”, Russian Math. Surveys, 74:3 (2019), 387–430  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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