Geometric realizations of birational transformations via $\mathbb{C}^*$-actions

TL;DR

This paper explores how varieties with torus actions can serve as geometric realizations of birational transformations, providing explicit constructions and analyzing their geometric properties like cones.

Contribution

It introduces explicit constructions of geometric realizations for a specific class of birational transformations using torus actions.

Findings

Explicit geometric realizations constructed for certain birational transformations

Analysis of Mori, Nef, and Movable cones of these varieties

Enhanced understanding of the geometric structure of transformations

Abstract

In this paper we study varieties admitting torus actions as geometric realizations of birational transformations. We present an explicit construction of these geometric realizations for a particular class of birational transformations, and study some of their geometric properties, such as their Mori, Nef and Movable cones.