I am not sure that this proof is correct for the following reason. If $ X^{\prime} $ is a non-singular surface and $ X $ is the blow-up of the surface at a non-singular point, then the sub-variety $ X \setminus V $ has codimension one in $ X $. This contradicts the result of step two, which says that $ X \setminus V $ is a closed set of codimension greater than or equal to two. In a thread, I asked about a generalization, and there is a possible revision of this proof that fixes this.

I am not sure that this proof is correct for the following reason. If $ X^{‘} $ is a non-singular surface and $ X $ is the blow-up of the surface at a non-singular point, then the sub-variety $ X \setminus V $ has codimension one in $ X $. This contradicts the result of step two, which says that $ X \setminus V $ is a closed set of codimension greater than or equal to two. In a thread, I asked about a generalization, and there is a possible revision of this proof that fixes this.

I am not sure that this proof is correct for the following reason. If $ X^{‘} $ is a non-singular surface and $ X $ is the blow-up of the surface at a non-singular point. The sub-variety $ X \setminus V $ has codimension one in $ X $. This contradicts the result of step two. In a thread, I asked about a generalization, and there is a possible revision of this proof that fixes this.

I am not sure that this proof is correct for the following reason. If $ X^{\prime} $ is a non-singular surface and $ X $ is the blow-up of the surface at a non-singular point, then the sub-variety $ X \setminus V $ has codimension one in $ X $. This contradicts the result of step two, which says that $ X \setminus V $ is a closed set of codimension greater than or equal to two. In a thread, I asked about a generalization, and there is a possible revision of this proof that fixes this.