Isomorphism among families of weighted K3 hypersurfaces

TL;DR

This paper demonstrates a one-to-one correspondence among certain families of weighted K3 hypersurfaces via explicit monomial birational morphisms, revealing isometric lattice polarizations and consistent Picard lattices.

Contribution

It explicitly constructs monomial birational morphisms among weighted projective spaces, establishing isomorphisms of lattice polarizations for weighted K3 hypersurfaces.

Findings

Weighted K3 hypersurfaces in certain families have isometric Picard lattices.

Constructed explicit monomial birational morphisms among weighted projective spaces.

Confirmed that Picard lattices of sublinear systems match those of complete linear systems.

Abstract

Some of the 95 families of weighted K3 hypersurfaces have been known to have the isometric lattice polarizations. It is shown that weighted K3 hypersurfaces in such families are to one-to-one correspond by explicitly constructing the monomial birational morphisms among the weighted projective spaces. All the weight systems having the isometric Picard lattices commonly possess an anticanonical sublinear system, being confirmed that the Picard lattice of the sublinear system we obtained is the same as those of the complete linear systems.