Generalized Abel-Prym maps and examples

Kelyane Abreu
Universidade Federal Fluminense (Brasil)
Abstract:
Let
\[C\]
be a smooth non rational projective curve over the complex field
\[\mathbb{C}\]
and let
\[(J(C), \Theta_C)\]
be its principally polarized Jacobian. If
\[A\]
is a subvariety of
\[J(C)\]
, we define the generalized Abel-Prym map
\[\varphi:C\rightarrow A\]
to be the composition of the Abel map with the norm map of
\[A\]
. In this talk we show some results about the degree of this map in the case where
\[A\]
is one of the components of the isotypical decomposition of the
\[J(C)\]
, and we will present some examples.