Computing the canonical height on K3 surfaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Computing the canonical height on K3 surfaces

Authors:	Gregory S. Call Joseph H. Silverman.

Affiliation:	address Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts 01002 ; address Department of Mathematics, Box 1917, Brown University, Providence, Rhode Island 02912

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 $hat{h} ^+$ and $hat{h} ^-$ 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 $sum _vhat{lambda} ^pm (,cdot ,,v)$ . 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 $hat{lambda} ^+(,cdot ,,v)$ , $hat{lambda} ^-(,cdot ,,v)$ , and the canonical heights $hat{h} ^+$ , $hat{h} ^-$ .

Keywords:	K3 surface canonical height

	点击此处可从《Mathematics of Computation》浏览原始摘要信息
	点击此处可从《Mathematics of Computation》下载全文