The structure of the prym map

Abstract

X r ~, ~--the subvariety of Ag parametrizing gacobians, birational image of ~g under the Jacobi map. curve of genus g. double cover of C. the Prym map. a semi-period on C. object whose Jacobian is p(C); a curve in Parts I-IV, a threefold in Part V. canonical map of X. Prym-canonical map of C. Abel map of X. Abel-Prym map of C. subvarieties of ~,, ~g where C is trigonal. subvarieties of ~g, ~g where C has an ordinary double point, C a Wirtinger double cover. ~E, RE--subvarietics of ~g, ~g where C has an elliptic tail and ~ is supported on the tail. ~s.s, ~s.s-Intersection of previous two. ~ar, ~ar --subvarieties of ~s, ~ where the elliptic tail E is harmonic (explained below). "me.a.n., ~e.a.n. --subvarieties of ~, ~s where the elliptic tail E is equianharmonic explained below).