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.
Citation
Markus Perling. "A lifting functor for toric sheaves." Tohoku Math. J. (2) 66 (1) 77 - 92, 2014. https://doi.org/10.2748/tmj/1396875663
Information