Explicit Computations on the Desingularized Kummer Surface

TL;DR

This paper derives explicit formulas for birational maps from a Kummer surface and its dual to their desingularization, explaining node blow-ups and automorphism groups, advancing understanding of their geometric structure.

Contribution

It provides explicit formulas for birational maps and describes the automorphism group of the desingularized Kummer surface, which was previously not well-understood.

Findings

Formulas for birational maps from Kummer surfaces to their desingularizations

Description of node blow-up process on the surface

Characterization of the automorphism group of the desingularized surface

Abstract

We find formulas for the birational maps from a Kummer surface K and its dual K^* to their common minimal desingularization S. We show how the nodes of K blow up. Then we give a description of the group of linear automorphisms of S.