Mori dream bonds and C∗${\mathbb {C}}^*$‐actions

Lorenzo Barban, Eleonora A. Romano, Luis E. Solá Conde and Stefano Urbinati

Mathematische Nachrichten, 2025, vol. 298, issue 4, 1127-1147

Abstract: We construct a correspondence between Mori dream regions arising from small modifications of normal projective varieties and C∗${\mathbb {C}}^*$‐actions on polarized pairs which are bordisms. Moreover, we show that the Mori dream regions constructed in this way admit a chamber decomposition on which the models are the geometric quotients of the C∗${\mathbb {C}}^*$‐action. In addition, we construct, from a given C∗${\mathbb {C}}^*$‐action on a polarized pair for which there exist at least two admissible geometric quotients, a C∗${\mathbb {C}}^*$‐equivariantly birational C∗${\mathbb {C}}^*$‐variety, whose induced action is a bordism, called the pruning of the variety.

Date: 2025
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