A cyclic cover branched over a curve of degree
A nonsingular degree hypersurface in .
All K3 surfaces are simply connected.
The Hodge diamond? is completely determined (even in positive characteristic) and hence the Hodge-de Rham spectral sequence? degenerates at . This also implies that the Betti numbers are completely determined as .
David Morrison, The geometry of K3 surfaces Lecture notes (1988)