Computing the canonical height on K3 surfaces
Abstract: Let be a surface in given by the intersection of a (1,1)-form and a (2,2)-form. Then is a K3 surface with two noncommuting involutions and . In 1991 the second author constructed two height functions and which behave canonically with respect to and , and in 1993 together with the first author showed in general how to decompose such canonical heights into a sum of local heights . We discuss how the geometry of the surface is related to formulas for the local heights, and we give practical algorithms for computing the involutions , , the local heights , , and the canonical heights , .
Gregory S. Call
Affiliation: address Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts 01002
Joseph H. Silverman
Affiliation: address Department of Mathematics, Box 1917, Brown University, Providence, Rhode Island 02912
Keywords: K3 surface, canonical height
Received by editor(s): August 2, 1994
Additional Notes: Research of the first author was partially supported by NSF ROA-DMS-8913113, NSA MDA 904-93-H-3022, and an Amherst Trustee Faculty Fellowship.
Research of the second author was partially supported by NSF DMS-9121727.
Article copyright: © Copyright 1996 American Mathematical Society