I want to know how to calculate nef cone of a GIT quotient. In particular let $X$ be a projective variety and $L$ be an ample line bundle on $X$ and $G$ be a reductive algebraic group and chosen a $G$ linearisation is it possible to calculate nef cone of $X//G$ if we know linear systems of $X$?
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1$\begingroup$ I do not think your question can be answered in such generality. However, if it helps, in this paper arxiv.org/abs/1702.00068 they computed several cones of divisors, in particular nef cones, of certain GIT quotients parametrizing configurations of points on $\mathbb{P}^1$. $\endgroup$– PuzzledJan 10, 2022 at 18:26
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$\begingroup$ Thanks for your comment..any example known or any other related papers are greatly appreciated. $\endgroup$– garyJan 11, 2022 at 5:28
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