2024/03/23 by Sally Andria, Andria, Sally, Jacqueline Rojas +3
#11A07 #14N10 #14N20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2403.15666
It is well-known that the Fermat surface of degree d≥ 3 has 3d2 lines. However, it has not yet been established what is the maximal number of pairwise disjoint lines that it can have if d≥ 4. In this article we show that the maximal number of skew lines on the Fermat surface of degree d≥ 4 is 3d, either d even or d odd distinct of 5, otherwise (d=5) it contains no more than 13 pairwise disjoint lines.