On the imbeddings of abstract surfaces in projective varieties

  title={On the imbeddings of abstract surfaces in projective varieties},
  author={Masayoshi Nagata},
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… 

Semiprojective completions of abstract curves

Every embedding of a variety V can be essentially accomplished by adjoining new representatives to V. When an embedding of V is obtained by adjoining representatives of some projective variety, we

Masayoshi Nagata (1927–2008) and his mathematics

Masayoshi Nagata, professor emeritus of Kyoto University, died of cancer in Kyoto on August 27, 2008, at the age of 81 years. He was born in the city of Ohbu near Nagoya and graduated from Nagoya

Abstract algebraic geometry