Parametrization of rational maps on a variety of general type, and the finiteness theorem

TL;DR

This paper introduces a natural parametrization of rational maps using linear projections, providing new geometric insights and improvements to the finiteness theorem for maps from fixed varieties to varieties of general type.

Contribution

It presents a novel parametrization approach for rational maps, enhancing understanding and results related to the finiteness theorem in algebraic geometry.

Findings

New parametrization via linear projections

Improved understanding of the geometry of the finiteness theorem

Enhanced results on the finiteness of rational maps

Abstract

In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing the natural parametrization of maps by means of the space of linear projections in a suitable projective space, and this leads to some new insight in the geometry of the finiteness theorem.