A note on polynomial maps having fibers of maximal dimension
Tom 166 / 2021
Colloquium Mathematicum 166 (2021), 129-136
MSC: Primary 12D10; Secondary 14E05, 52B11.
DOI: 10.4064/cm8162-8-2020
Opublikowany online: 9 March 2021
Streszczenie
For any two integers , 2\leq k\leq n, let f:(\mathbb {C}^*)^n\rightarrow \mathbb {C}^k be a generic polynomial map with a given Newton polytope. It is known that the points whose fiber under f has codimension 1 form a finite set C_1(f) in \mathbb {C}^k. We show that C_1(f) is empty if k\geq 3, we classify all Newton polytopes contributing to C_1(f)\neq \emptyset for k=2, and we compute |C_1(f)|.
