In this chapter, we give the definition of Mordell–Weil lattice (in Sect. 6.5). First, we bring
together the concepts from Chaps. 4 and 5 in order to gain a better understanding of the …

The notion of constant cycle curves on K3 surfaces is introduced. These are curves that do
not contribute to the Chow group of the ambient K3 surface. Rational curves are the most …

These notes grew out of a series of lectures given at Sogang University, Seoul, in October
2009. They were meant for complex geometers, who are not familiar with characteristic-p …

Given a K3 surface X over a number field K with potentially good reduction everywhere, we
prove that the set of primes of K where the geometric Picard rank jumps is infinite. As a …

Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c X on
X of degree 1 and Huybrechts proved that the second Chern class of a rigid simple vector …

We discuss some aspects of the behavior of specialization at a finite place of Néron–Severi
groups of K3 surfaces over number fields. We give optimal lower bounds for the Picard …

We survey crystalline cohomology, crystals, and formal group laws with an emphasis on
geometry. We apply these concepts to K3 surfaces, and especially to supersingular K3 …

We complete the remaining cases of the conjecture predicting existence of infinitely many
rational curves on K3 surfaces in characteristic 0, prove almost all cases in positive …

We show that the maximal number of (real) lines in a (real) nonsingular spatial quartic
surface is 64 (respectively, 56). We also give a complete projective classification of all …

Rational curves on K3 surfaces Page 1 Invent math (2012) 188:713–727 DOI 10.1007/s00222-011-0359-y
Rational curves on K3 surfaces Jun Li · Christian Liedtke Received: 14 January 2011 …