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Abstract. We define a quasiprojective reduction of a complex algebraic variety X to be a regular map from X to a quasiprojective variety that is universal with respect to regular maps from X to quasiprojective varieties. A toric quasiprojective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasiprojective reduction. Then...
Abstract. Mapping a locally free module on a scheme to its l-th tensor power gives rise to a natural map from the Grothendieck group of all locally free modules to the Grothendieck group of all locally free representations of the l-th symmetric group. In this paper, we prove some formulas of Riemann-Roch type for the behavior of this tensor power operation with respect to the push-forward homomorphism...
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