Normal Projective Varieties of Degree 5

Abstract

We list all the irreducible reduced linearly normal and nondegenerate normal projective varieties of dimension n and degree five defined over an algebraically closed field k of char(k)=0. In the smooth case, or when n = 2, we give also classification results for any algebraically closed field k of char(k) ≥0.

Key Words:

• Δ-genus
• Projective varieties
• Small degree
• Sectional genus

2010 Mathematics Subject Classification:

• 14C20
• 14Q10
• 14Q15
• 14M06
• 14M10

ACKNOWLEDGMENT

I would like to thank Prof. A. Laface for many interesting, stimulating, and useful discussions about algebraic geometry and for introducing me to the Magma algebra system.

Notes

Communicated by C. Pedrini.