Secant defectiveness of toric varieties

Abstract: The $h$-secant variety $Sec_{h}(X)$ of a non-degenerate $n$-dimensional variety $X\subset\mathbb{P}^N$ is the Zariski closure of the union of all linear spaces spanned by collections of $h$ points of $X$. The expected dimension of $Sec_{h}(X)$ is $Expdim(Sec_{h}(X)):= \min\{nh+h-1,N\}$. The actual dimension of $Sec_{h}(X)$ may be smaller than the expected one.

Let $N$ be a rank $n$ free abelian group and $M$ its dual. Let $P\subseteq M_{\mathbb Q}$ be a full dimensional lattice polytope and $X_P$ the corresponding toric variety.

In this talk we discuss a new technique to give bounds on the Secant Defectivity of $X_P$ using information from the polytope $P$. It is a joint work just submitted with Antonio Laface and Alex Massarenti.

algebraic geometry

Audience: researchers in the topic

Comments: The link for the google meet will be posted here a few days in advance.

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Brazilian algebraic geometry seminar

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