Lines on smooth polarized $K3$-surfaces

Abstract

For each integer $D\ge 3$, we give a sharp bound on the number of lines contained in a smooth complex $2D$-polarized $K3$-surface in ${\mathbb{P}}^{D+1}$. In the two most interesting cases of sextics in ${\mathbb{P}}^4$ and octics in ${\mathbb{P}}^5$, the bounds are $42$ and $36$, respectively, as conjectured in an earlier paper.

Substantially revised; finer and more complete results

References in corpus (3)

• Lines on quartic surfaces
• Lines in supersingular quartics
• Smooth models of singular $K3$-surfaces

Cited by in corpus (7)

• Smooth models of singular $K3$-surfaces
• Conics in sextic $K3$-surfaces in ${\mathbb{P}}^4$
• 24 rational curves on K3 surfaces
• Lines on K3-quartics via triangular sets
• 12 rational curves on Enriques surfaces
• Conics in Kummer quartics
• Conics on Barth--Bauer octics