Normal surfaces of degree 7 in ? n

Abstract

Let Y be a surface of degree 7 of the complex projective space ℙ n , linearly normal and not contained in any hyperplane of ℙ n . The purpose of this paper is to describe the normal singular surfaces of degree 7 embedded in ℙ n , as above. The main contribution of this paper is to describe all normal singular projective surfaces with sectional genus 4.