2 – Intro | Goals

Study of the $K3$ surfaces $X_t$ with $\mathrm{N}\mathrm{S}(X_t)$ isomorphic to the lattice with Gram matrix

$$\left(\begin{array}{ccc}2t& 0& 0\\ 0& -2& 0\\ 0& 0& -2\end{array}\right)$$

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

• Automorphism groups $\text{Aut}(X_t)$
• Upper bound on the number of orbits of $(-2)$-curves on $X_t$
  under the action of $\text{Aut}(X_t)$.

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