Cremona, Jonquières e o Dual Complementar de Newton

Abstract

The present work deals with the relationship between Newton’s dual complement and birational maps, which it originated in the works of B. Costa, A. Simis and A. Dória. Initially, it presented the necessary concepts of commutative algebra and algebraic geometry through algebraic optics. In sequence, it addressed Newton’s main, dual complementary theme and its properties, assuming that the sets of monomials satisfy the canonical constraint. And then, it discussed the relationship between birationality and Newton’s complementary dual, analyzing that the dual complements and preserves the elements of the Cremona group and the Jonquières maps subgroup.