Gluing determinantal Cremona maps

TL;DR

This paper investigates determinantal Cremona maps, focusing on their algebraic and geometric properties, especially the projective degrees of certain almost linear maps, through polynomial system resolution and convex geometry techniques.

Contribution

It introduces a novel approach combining polynomial system resolution and convex geometry to analyze determinantal Cremona maps and describes the projective degrees of specific almost linear cases.

Findings

Describes projective degrees of some almost linear determinantal maps.

Connects algebraic properties of base ideals with convex geometric methods.

Provides new insights into the structure of determinantal Cremona transformations.

Abstract

We study determinantal Cremona maps, i.e. birational maps whose base ideal is the maximal minors ideal of a given matrix $\Phi$, via the resolution of the polynomials systems defined by $\Phi$. Using convex geometry, this approach leads in particular to describe the projective degrees of some almost linear determinantal maps.