Flips and Flops Constructed by GIT Quotient

TL;DR

This paper classifies threefold flips and flops arising from GIT quotients of complete intersections in six-dimensional complex space, extending previous work and showing no new examples exist in higher dimensions.

Contribution

It extends the classification of GIT quotient flips and flops from hypersurfaces to complete intersections in six dimensions and proves finiteness of such examples in higher dimensions.

Findings

Classified all threefold flips and flops from GIT quotients in $\

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Abstract

Brown constructed a series of threefold flips given by the GIT quotient of a hypersurface in $\mathbb{C}^5$. In this article, we classify threefold flips and flops which are the GIT quotients of complete intersections in $\mathbb{C}^6$. We also show that there are no more new examples as GIT quotients of complete intersections in $\mathbb{C}^n$ with $n\geq7$.