Degree of Rational Maps versus Syzygies

TL;DR

This paper establishes a broad upper bound on the degree of generically finite rational maps between projective varieties, linking it to degrees derived from the Rees algebra of the base ideal, with various special cases extending prior results.

Contribution

It introduces a new general upper bound for the degree of rational maps using Rees algebra degrees, extending and unifying previous findings.

Findings

Derived a universal degree bound for rational maps

Connected the degree bound to Rees algebra properties

Extended previous results to broader cases

Abstract

One proves a far-reaching upper bound for the degree of a generically finite rational map between projective varieties over a base field of arbitrary characteristic. The bound is expressed as a product of certain degrees that appear naturally by considering the Rees algebra (blowup) of the base ideal defining the map. Several special cases are obtained as consequences, some of which cover and extend previous results in the literature.