Rational Curves on K3 Surfaces

Abstract

We proved the existence of rational curves in every linear system on a general K3 surface and that all rational curves in the hyperplane class are nodal on a general K3 surface of small genus.

34 pages, AMSLatex, To Appear on JAG

References in corpus (2)

• BPS States, String Duality, and Nodal Curves on K3
• Counting rational curves on K3 surfaces

Cited by in corpus (15)

• On the Severi varieties of surfaces in P^3
• A note on Severi varieties of nodal curves on Enriques surfaces
• Seshadri constants of $K3$ surfaces of degrees 6 and 8
• Nonemptiness of Severi varieties on Enriques surfaces
• Sheaves on surfaces and virtual invariants
• Curves of maximal moduli on K3 surfaces
• Construction de courbes sur les surfaces K3 [d'après Bogomolov-Hassett-Tschinkel, Charles, Li-Liedtke, Madapusi Pera, Maulik...]
• The chi-y genera of relative Hilbert schemes for linear systems on Abelian and K3 surfaces
• Nodal Curves on K3 Surfaces
• On the existence of curves with a triple point on a K3 surface
• Convergence of mean curvature flow in hyperkähler manifolds
• Severi varieties on blow--ups of the symmetric square of an elliptic curve
• On the birational geometry of Hilbert schemes of points and Severi divisors
• Mukai flops and Plücker type formulas for hyper-Kähler manifolds
• Limits of nodal surfaces and applications