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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 5, Pages 1001–1039 (Mi izv1285)  

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

Equivariant bundles on toral varieties

A. A. Klyachko


Abstract: Equivariant bundles on toral varieties are described in terms of filtrations which arise canonically in the fiber over a fixed point. The cohomology groups and characteristic classes are computed in terms of these filtrations, and problems of linear algebra which arise from them are discussed.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:2, 337–375

Bibliographic databases:

UDC: 512.7
MSC: 14F05, 14L32
Received: 03.02.1988

Citation: A. A. Klyachko, “Equivariant bundles on toral varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989), 1001–1039; Math. USSR-Izv., 35:2 (1990), 337–375

Citation in format AMSBIB
\Bibitem{Kly89}
\by A.~A.~Klyachko
\paper Equivariant bundles on toral varieties
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 5
\pages 1001--1039
\mathnet{http://mi.mathnet.ru/izv1285}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1024452}
\zmath{https://zbmath.org/?q=an:0706.14010}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 2
\pages 337--375
\crossref{https://doi.org/10.1070/IM1990v035n02ABEH000707}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Klyachko, “Moduli of vector bundles and numbers of classes”, Funct. Anal. Appl., 25:1 (1991), 67–69  mathnet  crossref  mathscinet  zmath  isi
    2. Allen Knutson, Eric Sharpe, “Equivariant sheaves”, Chaos, Solitons & Fractals, 10:2-3 (1999), 399  crossref
    3. Syu Kato, “Integral closure of invariant ideals, toroidal resolution, and equivariant vector bundles”, Journal of Pure and Applied Algebra, 204:1 (2006), 106  crossref
    4. Holger Brenner, “Looking out for stable syzygy bundles”, Advances in Mathematics, 219:2 (2008), 401  crossref
    5. M. Perling, G. Trautmann, “Equivariant primary decomposition and toric sheaves”, manuscripta math, 2010  crossref
    6. Jürgen Hausen, Hendrik Süß, “The Cox ring of an algebraic variety with torus action”, Advances in Mathematics, 225:2 (2010), 977  crossref
    7. Laura Costa, Pedro Macias Marques, Rosa María Miró-Roig, “Stability and unobstructedness of syzygy bundles”, Journal of Pure and Applied Algebra, 214:7 (2010), 1241  crossref
    8. Olivier Penacchio, “Mixed Hodge structures and equivariant sheaves on the projective plane”, Math. Nachr, 2011, n/a  crossref
    9. Thorsten Weist, “Torus fixed points of moduli spaces of stable bundles of rank three”, Journal of Pure and Applied Algebra, 2011  crossref
    10. Martijn Kool, “Fixed point loci of moduli spaces of sheaves on toric varieties”, Advances in Mathematics, 2011  crossref
    11. José Luis González, “Okounkov bodies on projectivizations of rank two toric vector bundles”, Journal of Algebra, 330:1 (2011), 322  crossref
    12. IUSTIN COANDĂ, “ON THE STABILITY OF SYZYGY BUNDLES”, Int. J. Math, 22:04 (2011), 515  crossref
    13. Aravind Asok, James Parson, “Equivariant sheaves on some spherical varieties”, ERA-MS, 18 (2011), 119  crossref
    14. José Luis González, “Projectivized Rank Two Toric Vector Bundles are Mori Dream Spaces”, Communications in Algebra, 40:4 (2012), 1456  crossref
    15. José González, Milena Hering, Sam Payne, Hendrik Süß, “Cox rings and pseudoeffective cones of projectivized toric vector bundles”, Algebra Number Theory, 6:5 (2012), 995  crossref
    16. J. Choi, “Genus Zero BPS Invariants for Local P1”, International Mathematics Research Notices, 2012  crossref
    17. Markus Perling, “Resolutions and Cohomologies of Toric Sheaves. The affine case”, Int. J. Math, 2013, 1307312123  crossref
    18. Martijn Kool, “Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces”, Geom Dedicata, 2014  crossref
    19. Mestrano N. Simpson C., “Moduli of Sheaves”, Development of Moduli Theory - Kyoto 2013, Advanced Studies in Pure Mathematics, 69, ed. Fujino O. Kondo S. Moriwaki A. Saito M. Yoshioka K., Math Soc Japan, 2016, 77–172  mathscinet  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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