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

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

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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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
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14. José Luis González, “Projectivized Rank Two Toric Vector Bundles are Mori Dream Spaces”, Communications in Algebra, 40:4 (2012), 1456
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
16. J. Choi, “Genus Zero BPS Invariants for Local P1”, International Mathematics Research Notices, 2012
17. Markus Perling, “Resolutions and Cohomologies of Toric Sheaves. The affine case”, Int. J. Math, 2013, 1307312123
18. Martijn Kool, “Euler characteristics of moduli spaces of torsion free sheaves on toric surfaces”, Geom Dedicata, 2014
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
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