most recent 30 from http://mathoverflow.net 2013-06-19T02:22:26Z http://mathoverflow.net/feeds/question/39533 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/39533/abel-jacobi-map-for-regular-fibered-surfaces Fede 2010-09-21T19:07:47Z 2010-09-21T19:07:47Z

<p>Let $f:C\to S$ be a regular fibered surface where $S=Spec(R)$, $R=dvr$. Assume $C$ has smooth geometrically integral generic fibre $C_K$. We also assume the existence of a section $x\in C(S)$. Let $J_K$ be the Jacobian of $C_K$ and $u_K:C_K\hookrightarrow J_K$ the Abel-Jacobi map sending $x_K$ to $0_{J_K}$. Let $N$ be the Néron model of $J_K$. Can we find an Abel-Jacobi map for $C$, i.e. a morphism $u:C\to N$ extending $u_K$? We also assume $C$ is not smooth! What if $C$ is only normal? Thank you!</p>