プリム多様体によるヤコビ分解 Decomposition of Jacobians by Prym Varieties〈1st ed. 2022〉

著者名：Lange, Herbert/Rodríguez, Rubí E.

Springer（2022/11/24発売）

• 言語：ENG
• ISBN：9783031101441
• eISBN：9783031101458

Description

This monograph studies decompositions of the Jacobian of a smooth projective curve, induced by the action of a finite group, into a product of abelian subvarieties. The authors give a general theorem on how to decompose the Jacobian which works in many cases and apply it for several groups, as for groups of small order and some series of groups. In many cases, these components are given by Prym varieties of pairs of subcovers. As a consequence, new proofs are obtained for the classical bigonal and trigonal constructions which have the advantage to generalize to more general situations. Several isogenies between Prym varieties also result.

Table of Contents

Introduction.- Preliminaries and basic results.- Finite covers of curves.- Covers of degree 2 and 3.- Covers of degree 4.- Some special groups and complete decomposabality.- Bibliography.- Index.