100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Eisenbud's conjecture on secant varieties to Veronese reembeddings

Lundi, 20 Septembre, 2010 - 16:00
Prénom de l'orateur : 
Jarek
Nom de l'orateur : 
BUCZYNSKI
Résumé : 

Let X be a subvariety in P^N and fix an integer r. The conjecture of
Eisenbud (for curves, known also as Eisenbud-Koh-Stillman conjecture)
tried to predict a uniform presentation of defining equations of r-th
secant variety to d-th Veronese embedding of X, provided d is
sufficiently large. I will explain the statement in details and I will
present several counterexamples to the conjecture, including curves with
very easy singularities, and a projective space P^N, with N at least 6,
and r at least 14. On the other hand, a much weaker version of the
conjecture is true and I will explain this as well. There is still quite a
big space between the known version and the counterexamples to
investigate. The talk is based on a joint work with Adam Ginensky and
Joseph Landsberg.

Institution de l'orateur : 
Institut Fourier
Thème de recherche : 
Algèbre et géométries
Salle : 
04
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