Degree of Rational Maps versus Syzygies
M. Chardin, S. H. Hassanzadeh, and A. Simis

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.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation
