# 2 – Intro | Goals

Study of the $K3$ surfaces $X_t$ with $\NS(X_t)$ isomorphic to the lattice with Gram matrix

$$\begin{pmatrix}2t & 0 & 0\\ 0 & -2 & 0\\ 0 & 0 & -2 \end{pmatrix}$$

For $1\leq t \leq 50$, we had to determine

• Automorphism groups $\aut(X_t)$
• Upper bound on the number of orbits of $\cu$-curves on $X_t$
under the action of $\aut(X_t)$.