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For a variety X which admits a Cox ring we introduce a functor from the category of quasi-coherent sheaves on $X$ to the category of graded modules over the homogeneous coordinate ring of $X$.
Sur les foncteurs dérivés de lim ← \underleftarrow{\lim} . Applications
J.-E. Roos · 1961
Earlier work this paper cites.
Les foncteurs dérivés de lim ← \varprojlim et leurs applications en théorie des modules
C. U. Jensen · 1972
Earlier work this paper cites.
Equivariant Completion, I
H. Sumihiro · 1974
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Stable Reflexive Sheaves
R. Hartshorne · 1980
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Convex Bodies and Algebraic Geometry
T. Oda · 1988
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Equivariant Bundles on Toral Varieties
A. A. Klyachko · 1990
Cited alongside, same era.
Vector Bundles and Torsion Free Sheaves on the Projective Plane
A. A. Klyachko · 1991
Cited alongside, same era.
Introduction to Toric Varieties
W. Fulton · 1993
Cited alongside, same era.
The Homogeneous Coordinate Ring of a Toric Variety
D. A. Cox · 1995
Cited alongside, same era.
Methods of Graded Rings
C. Năstăsescu and F. van Oystaeyen · 2004
Cited alongside, same era.
Graded Rings and Equivariant Sheaves on Toric Varieties
M. Perling · 2004
Later among the works it cites.
Equivariant Primary Decomposition and Toric Sheaves
M. Perling and G. Trautmann · 2010
Later among the works it cites.
Resolutions and Cohomologies of Toric Sheaves. The affine case
M. Perling · 2011
Closest in time.
Characterizing Serre quotients with no section functor and applications to coherent sheaves
M. Barakat and M. Lange-Hegermann · 2012
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