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arXiv · 2103.07209

Small modifications of Mori dream spaces arising from ${\mathbb C}^*$-actions

Gianluca Occhetta·Eleonora A. Romano·Luis E. Solá Conde·Jarosław A. Wiśniewski
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Abstract

We link small modifications of projective varieties with a ${\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Białynicki-Birula cells, we produce a system of birational equivariant modifications of the original variety, which includes those on which a quotient map extends from a set of semistable points to a regular morphism. The structure of the modifications is completely described for the blowup along the sink and the source of smooth varieties with Picard number one with a ${\mathbb C}^*$-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a ${\mathbb C}^*$-action associated to short grading of their Lie algebras.

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BibTeXRIS

Gianluca Occhetta, Eleonora A. Romano, Luis E. Solá Conde, Jarosław A. Wiśniewski. 2021-03-12. Small modifications of Mori dream spaces arising from ${\mathbb C}^*$-actions. https://doi.org/10.1007/s40879-022-00540-w

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