Secant varieties of toric varieties part 1

July 10, 2019
Versione stampabile
Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 9.45 a.m.
 
Reynaldo Staffolani - PhD in Mathematics
 
Abstract
Given a non degenerate irreducible projective variety $X$, its $2$-secant variety is defined as the Zariski closure of the union of the spans of any two points of the variety $X$. 
The aim of this talk is to study the $2 $-secant variety of some well known toric varieties.
 
In particular, given an $n$-dimensional smooth lattice polytope $P \subset 2 \Delta_n $, we will show that up to $AGL _n(\mathbb{Z})$-equivalence, it is one of $$\Delta_n,\quad 2\Delta_n,\quad(2\Delta_n)_k \; 0\leq k \leq n-2, \quad \Delta_l \times \Delta_{n-l}\; 1\leq l \leq n-1.$$
We will describe its corresponding toric variety $X_P $ and we will compute the dimension of its $2 $-secant variety.
 
 
The seminar corresponds to the final exam of Algebraic Geometry II, a planned course within  Staffolani's  first year PHD study programme  
 
Contact Person: Eduardo Luis Sola Conde