The Abel-Jacobi isomorphism for the sextic double solid

Giuseppe Ceresa and Alessandro Verra

Vol. 124 (1986), No. 1, 85–105

DOI: 10.2140/pjm.1986.124.85

Abstract

Let X be a double cover of P³ branched along a sextic surface S. Using a method of Clemens and Letizia, in this paper we show that, for general X, the Abel-Jacobi map associated to the surface F of curves contained in X which are preimages of conies “totally tangent” to S, induces an isomorphism between the Albanese variety of F and the intermediate jacobian of X.

Mathematical Subject Classification 2000

Primary: 14J30

Secondary: 14C30, 14K30

Milestones

Received: 30 November 1984

Published: 1 September 1986