On the imbeddings of abstract surfaces in projective varieties

@inproceedings{Nagata1957OnTI,
  title={On the imbeddings of abstract surfaces in projective varieties},
  author={Masayoshi Nagata},
  year={1957}
}
Recently Zariski proved that a normal abstract surface can be imbedded in a projective variety if (and only if) there exists an affine variety which carries all singular points of the variety! ) The main purpose of the present paper is to prove the following THEOREM 1. T here ex ists a complete normal surface which cannot be imbedded in any projective space. In order to prove Theorem 1, we shall prove the following two theorems, from which Theorem 1 follows easily : THEOREM 2. E v ery normal… 

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