Tomorrow's talk - reminder

[Fabio Perroni]

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SISSA GEOMETRY SEMINARS
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Prof. Remke Kloosterman (Humboldt Universitaet zu Berlin) will give a talk on

Ciliberto-Di Gennaro conjecture on non-factorial hypersurfaces

on Friday, March 7th, at 11:30 am in room 134, SISSA building A

Abstract:

In 2004 Ciliberto and Di Gennaro conjectured that a nodal threefold in  
$\mathbb{P}^4$ with at most $2(d-2)(d-1)$ nodes is either factorial or  
contains a plane or a quadric surface.

In this talk we present a proof for this conjecture.

We use Noether-Lefschetz theory for surfaces in $\mathbb{P}^3$ to  
prove that a non-factorial nodal threefold with at most $2(d-2)(d-1)$  
nodes contains a plane or a quadric surface unless it is birationally  
covered by lines. Then we use the classification of threefolds covered  
by lines to conclude that we are always in one of the first two cases.