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Tohoku Mathematical Journal
SECOND SERIES VOL. 66, NO. 1
|Tohoku Math. J.|
66 (2014), 77-92
A LIFTING FUNCTOR FOR TORIC SHEAVES
(Received October 14, 2011, revised February 26, 2013)
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 $X$. We show that this functor is right adjoint to the sheafification functor and therefore left-exact. Moreover, we show that this functor preserves torsion-freeness and reflexivity. For the case of toric sheaves, we give a combinatorial characterization of its right derived functors in terms of certain right derived limit functors.
Mathematics Subject Classification.
Primary 14L30; Secondary 13A02, 14M25.
Key words and phrases.
Toric varieties, Mori dream spaces, homogeneous coordinates, graded rings, toric sheaves.
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