2022/11/16 by Shoemaker, Mark · 1 citation
#14E99 #14L24 #14N35 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.09218
Kleiman's criterion states that, for X a projective scheme, a divisor D is ample if and only if it pairs positively with every non-zero element of the closure of the cone of curves. In other words, the cone of ample divisors in N1(X) is the interior of the nef cone. In this paper we present an analogous statement for a variety X acted on by a reductive group G with a choice of G-linearization L → X. In this new context, the ample cone of X is replaced by a cell in the variation of GIT decomposition of the G-ample cone, and curves in X are replaced by quasimaps to [X/G].