Tohoku Mathematical Journal
2014
March
SECOND SERIES VOL. 66, NO. 1

Tohoku Math. J.
66 (2014), 77-92

Title A LIFTING FUNCTOR FOR TORIC SHEAVES

Author Markus Perling

(Received October 14, 2011, revised February 26, 2013)
Abstract. 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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