Talks by Tommasi and Kloosterman

[Fabio Perroni]

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SISSA GEOMETRY SEMINARS
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Prof Orsola Tommasi (Leibniz Universitaet Hannover) will give a talk on

Cohomology of moduli spaces of genus 2 curves and the Gorenstein conjecture

on Wednesday, March 5th, at 11:30 am in room 133, SISSA building A

Abstract:

A main theme in the study of the cohomology of moduli spaces of curves  
is the study of the tautological ring, a subring generated by certain  
geometrically natural classes. An open question is whether the  
tautological ring is a Gorenstein ring, as conjectured by Carel Faber  
in the case of smooth curves without marked points. In this talk we  
discuss an approach that allows to detect the existence of  
non-tautological classes in the cohomology ring of the moduli space of  
stable curves of genus 2 with sufficiently many marked points, such as  
those constructed by Graber and Pandharipande for \bar M_{2,20}. We  
use this to prove that the Gorenstein conjecture does not hold for  
these spaces.
This is joint work with Dan Petersen (ETH Zuerich).

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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.