# K3 surfaces | Solutions

We provide computer-based solutions for the study of complex $K3$ surfaces.

Let $X$ be a complex algebraic $K3$ surface with Néron-Severi group $S=\text{NS}(X)$.

Study of the automorphism group of $X$,
Orbits of smooth rational curves

Denote by $\mathcal{P}_S$ the positive cone of $X$. Coming soon :

NB : The Poolized Borcherds’ method enforces parallelism at the level of the internal procedures of the Borcherds’ method. When we write “towards a parallelized Borcherds’ method”, we aim for also enforcing parallelism at the level of the Borcherds’ method itself: That is, parallelizing the exploration & processing of the chamber structure, while remaining able to make use of parallelism within the method, i.e., at the level of its core components, like in our Poolized implementation of the Borcherds’ method which takes advantage of process-based parallelism.

Study of projective models of $X$

MISC

NB : Many other things (which are neither mentioned on this site nor in the manuscript) were done during the thesis, such as : the determination of explicit equations of $K3$ surfaces using a computer-based approach, asymptotic study of the distribution of classes of smooth rational curves (power model, log model, exp. model…), application of Merten’s algorithm to generate automorphisms of $K3$ surfaces.