Let ℂ^* denote ℂ \{0}. Let k, ℓ∈ℕ. Prove that H^p(ℂ^k ×(ℂ^*)^ℓ, 𝒪)=0 for all p0.

Question

Let ℂ^* denote ℂ \{0}. Let k, ℓ∈ℕ. Prove that H^p(ℂ^k ×(ℂ^*)^ℓ, 𝒪)=0 for all p>0.

Accepted Answer

Step 1: Understand the context and the objects involved. We are working with the space u005C(u005Cmathbb

Let $\mathbb{C}^$ denote $\mathbb{C} \backslash\{0\}$. Let $k, \ell \in \mathbb{N}$. Prove that $H^p\left(\mathbb{C}^k \times\left(\mathbb{C}^\right)^{\ell}, \mathcal{O}\right)=0$ for all $p>0$.