26 citations · 125 across the 28 of their papers we have counts for
31 papers
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…
Lines on K3-sextics with simple singularities
Alex Degtyarev, Sławomir Rams
We advance our understanding of the configurations of low degree smooth rational curves on (quasi-)polarized complex K3-surfaces. We apply our efficient approach to classify the co…
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…
Miyaoka's bound for conics on K3 surfaces and beyond
Sławomir Rams, Matthias Schütt
We show that Miyaoka's bound for the number of conics on a degree-2h K3 surface is attained for high h, and analogously for higher even degree (smooth) rational curves.
Low degree rational curves on quasi-polarized K3 surfaces
Sławomir Rams, Matthias Schütt
We prove that there are at most low-degree rational curves on high-degree models of K3 surfaces with at most Du Val singularities, where is the number of exception…
Lines on K3-quartics via triangular sets
Alex Degtyarev, Sławomir Rams
We prove the sharp upper bound of at most lines on a complex K3-surface of degree four with a non-empty singular locus. We also classify the configurations of more than l…