Abstract:
In his work on the $0$-cycles on surfaces Mumford used a method of
induced differentials that was proposed by Severi, and introduced a
definition of a trace on differential forms. Lopez and Pirola apply
this method to the study of correspondences on surfaces. In my talk, I
will prove the following result of these two authors: if a smooth
surface $S$ of degree $d \geq 5$ in a three-dimensional projective space
is given, and $\Gamma$ is a correspondence with null trace of degree $n$ on $X
\times S$, then $n \geq d - 2$, and equality holds only if $\Gamma$ is
equivalent to one of the three ‘standard’ types of correspondences.
|
