We link small modifications of projective varieties with a 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 C∗-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a C∗-action associated to short grading of their Lie algebras.
Small Modifications of Mori Dream Spaces Arising from C∗ -Actions / Occhetta, G.; Romano, E. A.; Wisniewski, J. A.; Sola Conde Luis, E.. - In: EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 2199-675X. - 2022:(2022), pp. 1-33. [10.1007/s40879-022-00540-w]
Small Modifications of Mori Dream Spaces Arising from C∗ -Actions
Occhetta G.;Romano E. A.;Wisniewski J. A.;Sola Conde Luis E.
2022-01-01
Abstract
We link small modifications of projective varieties with a 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 C∗-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a C∗-action associated to short grading of their Lie algebras.File | Dimensione | Formato | |
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