Matching Tag: polynomial-mappings
Existence conjecture. Does there exist a function ρ \rho ρ
Fix an integer d ≥ 3 d\geq 3 d ≥ 3 n ≥ 1 n\geq 1 n ≥ 1 H = ( H i , α : i ∈ [ n ] , ∣ α ∣ = d ) H=(H_{i,\alpha}:i\in[n],\lvert\alpha\rvert=d) H = ( H i , α : i ∈ [ n ] , ∣ α ∣ = d ) Ψ i , j α ( H ) \Psi_{i,j}^{\alpha}(H) Ψ i , j α ( H )
Let F = ( f 1 , … , f n ) : R n → R n F=(f_1,\ldots,f_n):\mathbb R^n\to\mathbb R^n F = ( f 1 , … , f n ) : R n → R n J ( F ) J(F) J ( F ) S F S_F S F
Let G = ( G 1 , … , G n − 1 ) : C n → C n − 1 G=(G_1,\ldots,G_{n-1}):\mathbb{C}^n\to\mathbb{C}^{n-1} G = ( G 1 , … , G n − 1 ) : C n → C n − 1 n ≥ 2 n\geq 2 n ≥ 2 K 0 ( G ) = ∅ K_0(G)=\emptyset K 0 ( G ) = ∅
Let F : C n → C n F:\mathbb{C}^n\to\mathbb{C}^n F : C n → C n K 0 ( F ) K_0(F) K 0 ( F ) F F F S F S_F S F
Let P ( z ) = ( P 1 ( z ) , … , P q ( z ) ) P(z)=(P^1(z),\ldots,P^q(z)) P ( z ) = ( P 1 ( z ) , … , P q ( z )) z = ( z 1 , … , z n ) ∈ C n z=(z^1,\ldots,z^n)\in\mathbb C^n z = ( z 1 , … , z n ) ∈ C n A ( z , z ˉ ) A(z,\bar z) A ( z , z ˉ ) r r r
