Mori Dream Bonds and $\mathbb{C}^*$-actions
Lorenzo Barban, Eleonora A. Romano, Luis E. Sol\'a Conde, Stefano, Urbinati

TL;DR
This paper establishes a correspondence between Mori dream regions from small modifications of varieties and $ ext{C}^*$-actions on polarized pairs, revealing chamber decompositions and constructing bordisms via $ ext{C}^*$-equivariant birational models.
Contribution
It introduces a novel link between Mori dream regions and $ ext{C}^*$-actions, including chamber decompositions and a method to construct bordisms from given actions.
Findings
Mori dream regions correspond to $ ext{C}^*$-actions on polarized pairs.
Chamber decompositions of Mori dream regions relate to geometric quotients.
Construction of $ ext{C}^*$-bordisms from multiple geometric quotients.
Abstract
We construct a correspondence between Mori dream regions arising from small modifications of normal projective varieties and -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 -action. In addition we construct, from a given -action on a polarized pair for which there exist at least two admissible geometric quotients, a -equivariantly birational -variety, whose induced action is a bordism, called the pruning of the variety.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology
