

Iskovskikh Seminar
February 16, 2017 18:00, Moscow, Steklov Mathematical Institute, room 540






On the correspondence with null trace on surfaces
K. V. Loginov^{} 
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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 threedimensional 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.

