3 papers
math.AG2025
Periodic sharpness of Miyaoka's bound for smooth rational curves
Alex Degtyarev, Sławomir Rams
We determine the maximal number of smooth rational degree d curves on a complex K3-surface of degree 2n provided n is sufficiently large as compared to d>1. We obtain precise chara…
math.AG2025
On large configurations of lines on quartic surfaces
Alex Degtyarev, Sławomir Rams
We estimate the number of lines on a non-K3 quartic surface. Such a surface with only isolated double point(s) contains at most twenty lines; this bound is attained by a unique con…
math.AG2025
K3 surfaces of degree six arising from desmic tetrahedra
Alex Degtyarev, Igor Dolgachev, Shigeyuki Kondo
We study K3 surfaces of degree 6 containing two sets of 12 skew lines such that each line from a set intersects exactly six lines from the other set. These surfaces arise as hyperp…